Simplify √40x4y8

Simplify √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
checking for integer square root values below:

40 = √140
40 = √220
40 = √410
40 = √58

From that list, the highest factor that has an integer square root is 4.
Therefore, we use the product combo √40 = √410
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 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
2x2y410

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### What 4 formulas are used for the Radical Expressions Calculator?

List out all factor products for S
Find the highest factor with an integer square root and multiply the square root by the other square root of the factor

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### What 3 concepts are covered in the Radical Expressions Calculator?

The √ symbol that is used to denote square root or nth roots