Simplifying Radicals Cube Roots Calculator

How to Use This Calculator

Using the simplifying radicals cube roots calculator is straightforward. Follow these steps:

1. Enter the number you want to simplify in the input field.
2. Select whether you want to simplify a square root or a cube root.
3. Click the "Calculate" button to see the simplified form.
4. Review the result and the step-by-step explanation.

The calculator will display the simplified radical form and explain how it was derived. You can also use the "Reset" button to clear the inputs and start over.

Simplifying Radicals

Simplifying radicals involves expressing a square root in its simplest form by factoring out perfect squares. Here's how to do it:

1. Factor the number under the square root into its prime factors.
2. Identify any perfect squares in the factors.
3. Take the square root of the perfect squares and multiply them outside the radical.
4. Leave any remaining factors inside the radical.

For example, to simplify √72:

1. Factor 72 into 36 × 2.
2. 36 is a perfect square (6²).
3. √72 = √(36 × 2) = √36 × √2 = 6√2.

Simplifying Cube Roots

Simplifying cube roots involves expressing a cube root in its simplest form by factoring out perfect cubes. Here's how to do it:

1. Factor the number under the cube root into its prime factors.
2. Identify any perfect cubes in the factors.
3. Take the cube root of the perfect cubes and multiply them outside the radical.
4. Leave any remaining factors inside the radical.

For example, to simplify ∛54:

1. Factor 54 into 27 × 2.
2. 27 is a perfect cube (3³).
3. ∛54 = ∛(27 × 2) = ∛27 × ∛2 = 3∛2.

Worked Examples

Example 1: Simplifying √48

1. Factor 48 into 16 × 3.
2. 16 is a perfect square (4²).
3. √48 = √(16 × 3) = √16 × √3 = 4√3.

Example 2: Simplifying ∛108

1. Factor 108 into 27 × 4.
2. 27 is a perfect cube (3³).
3. ∛108 = ∛(27 × 4) = ∛27 × ∛4 = 3∛4.