Checking square roots, we see that 6^{2} = 36 and 7^{2} = 49. Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing 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

Simplifying our product of radicals, we get our answer: √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:

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