Simplify the following radical expression:
√40x4y8
Simplify the radical expression:
√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
√40 = √1√40
√40 = √2√20
√40 = √4√10
√40 = √5√8
The highest factor with an integer square root is 4
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 radicalWe 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
