Simplifying Nonperfect Roots Calculator

What is a Nonperfect Root?

A nonperfect root is a root of a number that doesn't result in a whole number. For example, √8 is a nonperfect square root because 8 isn't a perfect square. Similarly, ³√27 is a nonperfect cube root because 27 isn't a perfect cube.

Nonperfect roots can be simplified by factoring the radicand (the number under the root) into perfect powers and other factors. This process makes the root easier to understand and work with.

How to Simplify Roots

Simplifying roots involves several steps:

1. Factor the radicand into perfect powers and other factors.
2. Separate the root into the product of roots of the factors.
3. Take the roots of the perfect powers out of the radical.
4. Combine the results to get the simplified form.

For example, to simplify √72:

1. Factor 72 into 36 × 2 (since 36 is a perfect square).
2. Separate the root: √(36 × 2) = √36 × √2.
3. Take the square root of 36: 6 × √2.
4. The simplified form is 6√2.

Using the Calculator

Our calculator simplifies nonperfect roots for you. Enter the radicand (the number under the root) and select the root type (square root, cube root, etc.). The calculator will display the simplified form of the root.

The calculator uses the following formula to simplify roots:

For example, if you enter 72 as the radicand and select square root, the calculator will simplify √72 to 6√2.

Examples

Here are some examples of simplified nonperfect roots:

• √8 = 2√2
• √50 = 5√2
• √108 = 6√3
• ³√28 = 2³√7 = 2∛7
• ³√108 = 3³√4 = 3∛4