sqrt(x^5 y^2)+ sqrt(9xy^2)

Question

How would I simplify this?

Answer 1

Nevermind I figured it out it is sqrtx(x^2y+3y)

Answer 2

for ther first square root we can do the following:

Since y² has an even exponent, we can divide the exponent by 2 and put the y outside of the root.
x^5 can also by written as x*x^4. Since x^4 has an even exponent, we can divide the exponent by 2 and put x^2 outside of the root. So for the first root we get:

sqrt(x^5 y^2) = x²y sqrt(x)

For the second root we can follow the same procedure. Since sqrt(9) = 3 and sqrt(y²) = y, we can rewrite the second root as follows:

sqrt(9xy²) = 3y sqrt(x)

For the sum of the two roots, we get the following:

sqrt(x^5 y^2)+ sqrt(9xy^2) =
x²y sqrt(x) + 3y sqrt(x) =
(x²y + 3y) sqrt(x)

So the answer is:

(x²y + 3y) sqrt(x)