sqrt(x^5 y^2)+ sqrt(9xy^2)
How would I simplify this?
Nevermind I figured it out it is sqrtx(x^2y+3y)
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)
To simplify the given expression: √(x^5 y^2) + √(9xy^2)
1. Start by identifying any perfect squares within the radicands (expressions under the square roots).
Notice that x^5 can be simplified as (x^2)(x^2)(x) and y^2 can be simplified as (y)(y).
Now, rewrite the expression as: √(x^2 x^2 x y y) + √(9xy^2)
2. Simplify each square root separately.
For the first square root, √(x^2 x^2 x y y), we can simplify this further. Take the square root of each perfect square separately and leave any non-perfect squares under the root: x x y √x
For the second square root, √(9xy^2), we can simply take the square root of 9 (which is 3) and leave the rest under the root: 3y √x
3. Combine the simplified square roots:
Putting it all together, the simplified expression becomes:
√(x^5 y^2) + √(9xy^2) = xy√x + 3y√x
So, the simplified expression is xy√x + 3y√x.