Simplify √

40x^{4}y^{8} Simplify √

40.

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√

10Our final answer is the factored out piece and the expression under the radical

**2x**^{2}y^{4}√10[+] __Watch the Radical Expressions Video__