Question

What is the simplified form of the following expression? 2(^4 sqrt 16x)- 2(^4sqrt2y)+3(^4sqrt81x)-4(^4sqrt 32y) Assume x>0 and y>0

Answer 1

If it's on edge, the answer is C.

Answer 2

For this case we have the following expression:
2 (^ 4 sqrt 16x) - 2 (^ 4sqrt2y) +3 (^ 4sqrt81x) -4 (^ 4sqrt 32y)
Rewriting we have:
2 (^ 4 sqrt 2 ^ 4x) - 2 (^ 4sqrt2y) +3 (^ 4sqrt3 ^ 4x) -4 (^ 4sqrt 2 ^ 4 * 2y)
Then by root properties we have:
2 * 2 (^ 4 sqrt x) - 2 (^ 4sqrt2y) + 3 * 3 (^ 4sqrt x) -4 * 2 (^ 4sqrt 2y)
Rewriting:
4 (^ 4 sqrt x) - 2 (^ 4sqrt2y) + 9 (^ 4sqrt x) - 8 (^ 4sqrt 2y)
Adding similar terms:
13 (^ 4 sqrt x) - 10 (^ 4sqrt2y)
Answer:
13 (^ 4 sqrt x) - 10 (^ 4sqrt2y)