How to solve this problem without calculator?|| A Nice Olympiad mathematics. 

Thank you sir for this nice solving

You have done it very long process.Nice solution.

The solution is just of 3 lines😂

x^2 = (4)(6)(8)(10) + 16 = (16)(120 + 1) = (4^2)(11^2) = 44^2; x = +/- 44

The same problem, solved without calculator or paper (this can all be done in head) x^2-16=4x6x8x10 (have to avoid the asterix or youtube will parse it as formatting) 4x6x8x10 = (2^2)x(2x3)x(2^3)x10 = 2^6 x 3 x 10 = 64 x 3 x 10 = 1920 x^2-16=1920 x^2=1936 seeing as 40^2=1600 and 50^2=2500, x is going to be a two-digit number starting with 4 using (a+b)^2=a^2+2ab+b^2: 40^2+80b+b^2=1936 b^2+80b=336 Given that b is a one digit number, the 80b will be most of its value. 80x4 is very close to 336, so let's try 4: 4^2+80x4=336 16+320=336 this is true so b=4 so x=44 and x2=-44 will also solve this equation now let me watch the video.