sqrt(40x^4y^8)

<-- Enter expression (use sqrt for square root)
  

Simplify √40x4y8

Simplify √40.

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 = √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

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
2x2y410


What is the Answer?

Array

How does the Radical Expressions Calculator work?

Evaluates and simplifies radical expressions. Simplifying radical expressions.
This calculator has 1 input.

What 4 formulas are used for the Radical Expressions Calculator?

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

For more math formulas, check out our Formula Dossier

What 3 concepts are covered in the Radical Expressions Calculator?

radical
The √ symbol that is used to denote square root or nth roots
radical expressions
an nth root of a number x is a number r which, when raised to the power n, yields x
n√x
square root
a factor of a number that, when multiplied by itself, gives the original number
√x

What are some example calculations for the Radical Expressions Calculator?

  1. 2sqrt(28) + 3sqrt(63) - sqrt(49)
  2. sqrt(40x^4y^8)
  3. sqrt(2/16)+sqrt(98/9)

Radical Expressions Calculator Video


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