Simplify √
40x4y8 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√10Therefore, 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 ÷ 2y
8 ÷ 2 = x
2y
4Our leftover piece under the radical becomes 2√
10Our final answer is the factored out piece and the expression under the radical
2x2y4√10[+] Watch the Radical Expressions Video
