Well OK. That's very tricky and all. But isn't it easier to do some factoring instead? Factoring the value inside the square root, I get 2 * 5 * 2^2 * 3 * 2^4 * 2 * 3^2 + 36 Combining, I get 2^8 & 3^3 * 5 + 36. Notice that the product is divisible by 36, to divide it all by 36 and put "6" outside the square root: 6 * sqrt(2^6 * 3 * 5 + 1). 64 * 15 = 960, then add 1 to get 961. This turns out to be 31^2. Take it out of the square root to get 6 * 31 = 186. It's not hard, doesn't need a calculator or algebra.
Thanks, mate. Great work.
Well OK. That's very tricky and all. But isn't it easier to do some factoring instead? Factoring the value inside the square root, I get 2 * 5 * 2^2 * 3 * 2^4 * 2 * 3^2 + 36
Combining, I get 2^8 & 3^3 * 5 + 36. Notice that the product is divisible by 36, to divide it all by 36 and put "6" outside the square root: 6 * sqrt(2^6 * 3 * 5 + 1).
64 * 15 = 960, then add 1 to get 961. This turns out to be 31^2. Take it out of the square root to get 6 * 31 = 186. It's not hard, doesn't need a calculator or algebra.
10 = x
x(x+2)(x+6)(x+8) + 36
x(x+8) = x^2 + 8x
(x+2)(x+6) = x^2 + 6x + 2x + 12 = x^2 + 8x + 12
x^2 + 8x = y
(x^2 + 8x)(x^2 + 8x + 12) + 36
(y)(y + 12) + 36
y^2 + 12y + 36 (y + 6)^2
√(y+6)^2
y + 6 (y = x^2 + 8x)
x^2 + 8x + 6 (x = 10)
10^2 + 8.10 + 6
100 + 80 + 6
186