Checking square roots, we see that 62 = 36 and 72 = 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:
√x4y8 = x4 ÷ 2y8 ÷ 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
