sqrt(40x^4y^8)

Simplify √40x⁴y⁸

Simplify √40.

Checking square roots, we see that 6² = 36 and 7² = 49.
Our answer is not an integer.
Simplify it into the product of an integer and a radical.

List each product combo of 40
checking for integer square root values below:
√40 = √1√40
√40 = √2√20
√40 = √4√10
√40 = √5√8

From that list, the highest factor that has an integer square root is 4.
Therefore, we use the product combo √40 = √4√10
Evaluating square roots, we see that √4 = 2

Simplify our product

√40 = 2√10

Therefore, we can factor out 2 from the radical, and leave 10 under the radical

We can factor out the following portion using the highest even powers of variables:

√x⁴y⁸ = x^{4 ÷ 2}y^{8 ÷ 2} = x²y⁴
Our leftover piece under the radical becomes 2√10
Our final answer is the factored out piece and the expression under the radical
2x²y⁴√10