(The square root of 8 plus 1) divided by the square root of 8 =? Basic Algebra! 

Too much bla, bla, bla.

It doesn't require an 18 minute explanation !

Congratulations -- you made a simple process very complicated. ----> (4 + sqrt(2))/4

Here's an idea. How about getting right to solving (simplifying) the problem instead of showing us 5 ways how NOT to solve it? 95% of those who will take the time to watch the solution akready understand the concepts of identity and distribution, so it's not necessary to show us. For the few who don't , refer them to a separate tutorial about those things, and when they are good with that, THEN they can come back and apply those concepts to this problem. 90% of this video is a waste of time for 95% of the viewers.

You made this more complicated than necessary. An equally valid answer is 1 + 1/2*sqrt (2) and you can get there in 3 steps (Sqrt(8) +1)/sqrt (8) = sqrt (8)/sqrt(8) + 1/sqrt(8) Simplifying you get 1 + 1/sqrt(8) = 1 + 1/2sqrt(2)

When you say, "Can you solve?," that means, "What is the numerical value of this expression?" In this case, it is 1.3536. The question should be, "Can you reduce this expression?" For some reason, the presenter has an obsessive attachment to the idea that no expression should have a radical in the denominator. It's almost as bad as his near obsession with PEMDAS. In the Real World, where we want to see numbers, it makes absolutely no difference if there is a radical in the denominator or not.

no wonder so many people don't like math....if you need help falling asleep, this is a good vid to watch...

Simplify, not solve (in the title) please.

This is a joke right ?

All you get is another formula. What is that in practical terms? Would it not be 1.353....?

How about 1 + (square root of 2 ) divided by 4 ???

It seems very long😂

Far too much talking

I guess I don't understand how the "answer" is really any better than the "problem".

Whilst it is true that (√8+1)/√8 is the same as (4+√2)/4, the idea that the first one is a question and the second one is the answer is just silly.

If this is the correct answer, I would suggest the question should be: "Can you simplify to a common rational denominator?" I'm not sure how either the answer given or 1 + sqrt(2) / 4 "solves" the problem.

Could you make it any harder.

Solve??? No one can solve this because it is simply an expression, not something that can be solved such as an equation. Really shocking and disappointing that a math teacher doesn’t know the difference between solving and simplifying. Typical sloppy, irresponsible wording by someone who cares only about “likes” and “views” and has little or no interest in imparting knowledge.

This can be simplified in five lines in less than 10 seconds.

Solve? Is it equation? I don't think so.

Answer starts at 8:10

Quanta enrolação para resolver um problema elementar. Fala sem parar

I would have separated the numerator into two terms rationalizing the second term and left the answer as 1+ (sqrt(2)/4).

Seems far simpler and clearer to just start with breaking the expression into the sum of 2 fractions √8/√8 + 1/√8, which is (1 + 1/√8) and then simplify to 1 + √2/4

You can also change sqrt(8) to 2*sqrt(2): (2sqrt(2) + 1)(sqrt(2)) ------------------------------- (2sqrt(2) (sqrt(2)) (2sqrt(2)sqrt(2)+(sqrt(2)) ------------------------- (2sqrt(2)(sqrt(2)) (2 * 2) + sqrt(2) ------------------------ (2sqrt(2)sqrt(2)) 4 + sqrt(2) ----------------- 4 1 + sqrt(2) ---------- ✅✅✅ 4

Wouldn't 1 + √(2)/4 be simpler? Seems weird to include the 4/4

Rewrite: (8 ^ 1/2) / (8 ^ 1/2) + (1) / (8 ^ 1/2) . The first set Cancels out Leaving 1 + (1/8 ^ 1/2) We have a root in the denominator so we multiply the top and bottom by it: 1 + (1 * 8^ 1/2) divided by (8 ^ 1/2)² 1 + 2(2^1/2) / 8 The 1 is NOT affected by the denominator AND we can reduce the second part: 1 + (2^1/2) divided by 4 Technically the answer the professor gave is correct, BUT some (teachers like me) would mark that wrong because it wasn't FULLY reduced. When you have a fraction as an exponent the numerator is a power and the denominator is the root. Also Remember the rule (x + y ) divided by (x) is the same as x divided by x + y divided by x. This is valid since both parts of the numerator are affected by the denominator. Super simple and any of my passing 8th grade students would be able to solve this before going on Christmas break.

There isn't a solution to an expression. You might simply it if clearly stated rules describing simplest forms are given first.

I really don't know what you are saying. You give us an expression, not an equation and you ask us to solve it? What are you up to?

Only when I have luxury of time then I would waste to watch his lectures and not to the fullest but skipping. However, if he cuts down unnecessarily talking and examples he would be the best of all.

Is not a more elegant solution ...... 1+ 8 to the power -1/2 ?

you lost me.

What I'd like to know is how the answer is the problem simplified. All that work and still the answer is not simplified.

Good explanation for beginners. The truth is math often gets reduced to a series of tricks to squeeze out the answer. If you don't know the tricks it is difficult to intuitively find the answers. Yes, math people call them rules but essentially they are the tricks to solving equations. Students looking for a more straight forward process are often confused when confronted with these situations. Compounding the issue is there may be multiple ways of finding alternate forms of the answers. Often successful math skills come down to "training" the person to answer a problem in a certain way similar to Pavlov teaching his dogs. Not kind but often true.

Multiply top and bottom by sqrt(8). Get 8 as the denominator (rationalize 🤓), multiply out the nominator to 8 + sqrt(8), and go from there. Not yet watched the vid, but I feel a bit more can be done. However, for the purpose of the exercise, I guess, the denominator, I’d give at least 80% credit at this stage 😎

Or if you separated the two terms, you could have 1+((1/4)sqrt(2)).

No one thinks the answer is 1. This was way more confusing than it needed to be.

2 sqre root 8 +1

Gave you a like. What's crazy about Algrebra, you can start off reducing something, but it could be out of order. For example, suppose you decided to reduce both of the sqrt(8) to 2*sqrt(2) first. That is not the right way to solve this but it is a valid algebraic method. In this case it won't be a problem, but in many cases doing something in the wrong order may give you the wrong answer or "stump" you. Yes, memory tricks like PEMDAS, FOIL, SOHCAHTOA are there for simple things, but there are no memory tricks to take any equation and in what order do the "multitude" of things in your "bag of tricks" to reduce or solve it. I aced Algrebra/Geometry/Trigonometry but didn't retain things (swiss cheese) over the years... miss just one of the multitudes of rules and/or miss when to do them and... bingo... error/frustration. Algrebra makes sense to me, but there is just soooo many rules that fade with time (unless you are a mathematician). One would think there could be a single "algorithmic" approach to work any equation, but I started to try that and it was mess. So, sadly, you have get a "feel" on how how to solve something.... and to say I've seen this before - which would require you to do algebra virtually all day long 24/7 for your whole life. And Calculus even adds more rules and ordering. But people score well on the math in SATs becuse all the practice questions used in study guides and SAT prep classes are centered on identifying the "types" of problems and being prepared to solve only those... you've seen that before in study. You can get Ds in Algrebra, but study only the types used on SATs and you can do well. I solved my dilemma by buying a TI-92+ calculator that solves algebra and calculus problems using symbology just like we use in math ("pretty print" as they call it). There has to be a better way to burn EVERY rule and order into the brain... to be flawless in math, you MUST know it all COLD... else you get wrong answers and then what is the point.

...Which is (sqrt(8)+1)/sqrt(8), which evaluates to approximately 1.353553. Either form, or even 1+sqrt(2)/4, can be crunched to approximately 1.353553 equally as easily.

Ans=√8/√8+1/√8=1+1/√8.

Working with perfect squares, multiplying by sqrt2/sqrt2, would give (sqrt16+sqrt2)/sqrt16 = (4+sqrt2)/4, or 1+(sqrt2)/4?

(4+ sqrt 2)/4 is not finished. By partial fraction decomposition it becomes 1 + (1/(2* sqrt 2)). Like this. Sqrt 8= 2 * sqrt 2. ((2 * sqrt 2)+1)/(2* sqrt 2) Decompose, the 2 sqrt 2's cancel, Leaving (1 + (1/(2*sqrt 2))

Annoyingly unnecessarily long winded!!

Reduction to the absurd: imagine that the original problem simply was: Simplify SQRT(8). SQRT(80) divided by SQRT(10) would be an unlikely answer. Similarly 2 * SQRT(2) is more likely labelled as simpler, but is it really simpler? If I didn't know the SQRT(2) by memory, then SQRT(2) is just as difficult as SQRT(8). When I know SQRT(2) by memory, is it any worse being in the denominator? What I am trying to say is that mathematics is a science of numerical facts. Rating things on their simplicity is not a science. If we labelled these simplification exercises as a means to restate the problem without the value judgment, without the right vs. wrong judgment, wouldn't that be the spirit of mathematical science?

break it down even further 1 + 1/4 x sqrt 2

Damnit bogged down in minutiae again. STOP GETTING LOST IN THE WEEDS. Show us the solution then get into the unnecessary details. I get so mad at this crap I want to break something. But a new iPad is too expensive.

I came here for my daily nap. Wake me when he gets to the problem... Short, and concise is key to NOT confusing your students. I had it figured, then he rambled for ten minutes and now I'm confused(says almost every 14 year old).

There was a lot of discussion about what algebraic rules could be used in solving this problem.The most common questions concerned dividing the numerator sqrt(8) by the denominator sqrt(8). You can solve the problem this way, but must realize that this single fraction is the combined result of two fractions separate fractions-each with the common denominator of the sqrt(8). So, the combined fraction must be expanded back to the original rational terms with the correct radical terms. This will also ensure that the denominator is rationalized (note that the sqrt(8) in the original equation is not rationalized because its solution include the term sqrt(2). Here’s the solution version that divides the sqrt(8) by the sqrt(8). Just be aware of the rules and it’s easy: 1. Expand the fraction using its common denominator of sqrt(8): Sqrt(8) 1 ---- + ---- Sqrt(8) Sqrt(8) 2. Now simplify the two fractions: 1 1 + ---- Sqrt(8) 3. Simplify the Sqrt(8): 1 1 +. ----- 2*sqrt(2) 4. Simplify by multiplying by one, in this case the Sqrt(2) / sqrt(2): 1 1 Sqrt(2) + ----. * ----- 2*sqrt(2). Sqrt(2) 5. Eliminate or combine terms: 1 Sqrt(2) -- + ---------- 2*sqrt(2)*sqrt(2) (2 * 2 = 4) 6. Combine to one fraction using the new common denominator of 4: (4) Sqrt(2) --- + ---- (4) 4 7. Solution: a new common, rationalized denominator of 4. We followed algebraic rules that allowed us to divide the sqrt(8) into itself. 4 + Sqrt(2) -------- 4 Regards, Eric

Congratulations, you simplified the original problem, but that doesn’t give us an actual answer. We would still need to use a calculator to find the value. Which we could have done in the first place without all of the simplification. By the way the answer is 1.3535…

Before I clicked, I thought, over 18 mins?? How do you fill 18 min with this? After I clicked, I watched a while. I didn't finish. Too much talk, too much doodling, not enough to the point.

Find the comment section interesting. Very few understand the point of this channel. The point is to explain math in a way so even someone with zero mathing abilities will understand. So many want to show off their minimal knowledge and say nonsense like, “I did this in minus 3 moves. That’s how good I am”. All sorts of pathetic. Just keep on keeping on.

After 18 minutes of work, the "teacher" comes to a "simplification" that is not any easier than the original. Worse than that, a student who is trying to follow all the steps has no idea that each of the steps is not at all the only step that is required, leaving them thinking that math is a deep and dark mystery. When I first read the problem, I had no idea what the "teacher" would do to make it "simpler". That is, the answer to the original problem has not been found even after 18 minutes. AND, all the math in the problem remains, because if you are not using a calculator, how does the student get the square root of 2? If they are using the calculator, they might as well get the square root of 8. So..."teacher"...if you didn't start off with multiplying by root 8 over root 8, what would you have done? How do you explain the alternate choices to the student?

1 + (1/sqrt(8)) =1+ sqrt(8)/8 oops 1 +(sqrt(8)/8)

a square root in the denominator is not considered fully simplified in mathematical practice. Instead, you should rationalize the denominator to eliminate the square root. The answer is 1 + sq rt 2 over 4 Sq rt 8 = 2 x sq rt 2

As you can see by the many answers below, there is no single answer to this question. There are many equivalent ways to re-write the problem. There are many different ways to get to some answer. Is one answer simpler than another? Is one answer simpler than the original problem? Is a calculator still required to actually compute a number. I posed the original problem to my wife, and told her of the first step of multiplying by one. Her first response was like that of any inquisitive student...why would you do that? One person suggests "to rationalize the denominator" which leads to the most obvious question of ....why do you have to do that? If you say "to make it simpler" the obvious question is why would a sqrt 8 in the numerator be better than one in a denominator? , etc.etc. These questions have the pretense that there is a right answer and a right way to get there , making the student feel inadequate when they have attempted something else and when they fail to see that the answer is "simple".

Basic surds. Multiply by sqrt8/sqrt8 to rationalise the denominator….all over in less than 20 seconds for a student just starting surds.

Time wasting and unnecessarily talkative for such elementary school problem. Very boring

Mathematicians are always “rationalizing” their beliefs. Lol😊

wow, it must be 1 + 1/sqrt8 it is said that maths skills in America are a scandal among the Earth's nations bless this dude for attempting to rectify that But in reality its probably a lost cause

What is the rationale for too much rambling? Aren't you disorienting the learner?????

I don't think so, teacher gonna do that your solution cuz I don't agree what you solve that problem

It took you longer than you need. You are not a good teacher. 18 minitutes for a 1 minute problem.

You are very bad math teacher your explanation is bad this problem could solve a lot easier and simpler

I feel for your class, How can a maths teacher waffle this much? Unbelievable!

You purposely use a more complicated way to solve this , lot of talking for no apparent reason

There is nothing to “solve “because there is no =. in math, language is important.

Ajab khan khattak. Deviation...........deviation to arrive at evaluation.

Stop talking!!! Stop repeating! Stop painting! 🤬🤬🤬

For heaven's sake don't waste time by using unwanted explanations

You are wasted my 15 minutes for watch this stupid solution. I would just simply leave it as 1 + 1/ sq root of 8. Instead of you doing much ado about too many steps that getting same thing

sorry but there got to be a better way to explain this problem! I get it that the instructor knows how to but his job is to make math EZ so we don't have to use calculators and computers for simple problems!

Oh man I got 1+sqrt2/4 I guess I better keep studying.

Thank you. I home school my son, so I love to keep up with my Math Skills. I keep telling him that math in our language is known as " Mathafu" which deriveds from the word "Ma" meaning truth. This is commom in Bantu. It all comes from ancient Kemet, when the Atlantians, Tehuti and the rest of them arrived to teach the Kemites the truths and universal laws of the universe.

Why wouldn't you make it 1 + (√2/4)? Doesn't the distributive property work in subtraction too? (4+√2)/4 would become 4/4 + √2/4, which would reduce to 1 + √2/4. You could look at it as distributing 1/4 times the components of the numerator.

Solve or simplify? The genius at work again.

You can't solve this problem but you can simplify by rationalizing the denominator.

I like the info but it's too long winded,

So contorted! Gives one a headache. over such simple exercise.

Only NERDS need this information!!😆

(√8+1)/√8 equals √8/√8+1/√8 equals 1+1/√8. Why is that not considered fully simplified?

I'm so lost. I'm glad it's not a lesson on maps. I'll end up in Antarctica

He talks too much. Makes a simple problem complicated.

Stop explaining too much.Getting bored.

WTH do you complicate so much the explanation?

(√8 + 1) / √8 = (8 + √8) / 8 = 1 + 2√2 / 8 = 1 + √2 / 4.

my first answer would be 1+1/sqrt(8)

1+2√2/8 becomes 1+√2/4 That is the correct answer for simplification. NOT (4+√2)/4

simple just cancel out the sq of 8 leavrs answer 1

very poor and unwanted lengthy explanation

Christ's suffering wasn't this drawn out.

Too long, too much bla bla I nearly fall asleep.

so, what is the answer ? (mine is 5/4sqrt2 )

Bla Bla, I lost interest after 40 seconds,

Too long drawn, likes the sound of his own voice

Too much talk!

Sorry 2 sqre root or 2 =8 over 2 square root of 2

1+V2/4.

Huinya

Sehr langweilige Erklärung, viel zu viel Worte