# Simplifying Radicals Calculator

Simplifying Radicals Calculator is an online tool that calculates the simplified radical expression of the entered values. A radical expression can be defined as an algebraic expression that comprises radicals.

## What is a Simplifying Radicals Calculator?

Simplifying Radicals Calculator helps to express the given radical in its simplest form and remove the radical completely if possible. To simplify a radical expression we reduce the n^{th} root to its simplest form. To use the * simplifying radicals calculator*, enter the values in the input boxes.

### Simplifying Radicals Calculator

## How to Use the Simplifying Radicals Calculator?

Follow these steps to simplify the radical expression using the online simplifying radicals calculator.

**Step 1:**Go to Cuemath's online simplifying radicals calculator**Step 2:**Enter the values of the radical expression in the given input boxes.**Step 3:**Click on "**Calculate**" to find the simplified value of the radical.**Step 4:**Click on "**Reset**" to clear the fields and enter new values.

## How Does Simplifying Radicals Calculator Work?

A radical expression consists of roots of either variables or numbers. These roots could be square roots, cube roots or n^{th} roots. Let us suppose our radical expression is in the form of a ⁿ√x. Here, 'a' is a constant term and x is in the number under the radical. ⁿ√x denotes that we are dealing with the n^{th} root of x. The steps to simplify this expression are as follows:

- Step 1: Express the number x as a product of its prime factors.
- Step 2: Start grouping factors that have the same value in powers of n.
- Step 3: The factors that have the power of n can be written outside the radical sign. Once the factor is shifted out of the radical sign its corresponding exponent gets removed.
- Step 4: Now multiply all the factors that have been taken out of the radical sign with 'a'.
- Step 5: Finally, determine the n
^{th}root of the expression left under the radical. Multiply this with the remaining expression to get the final value.

## Solved Examples on Simplifying Radicals

**Example 1:** Simplify the radical \(4\sqrt[4]96 \) and verify it using the online radical calculator.

**Solution: **

Let us write the prime factor of the number within the radical and simplify it further.

\(4\sqrt[4]96 \) = 4\(\sqrt[4]{2\times 2 \times 2 \times 2 \times 2 \times 3}\)

= 4\(\sqrt[4]{ 2^{4} \times 2 \times 3}\)

= 4 × \(2\sqrt[4]{6}\)

= 8 \(\sqrt[4]{6}\)

\(\sqrt[4]{6}\) = 1.56

\(4\sqrt[4]96 \) = 8 × 1.56 = 12.52

**Example 2:** Simplify the radical \(7.2\sqrt[5]3125 \) and verify it using the online radical calculator.

**Solution: **

Let us write the prime factor of the number within the radical and simplify it further.

\(7.2\sqrt[5]3125 \) = 7.2\(\sqrt[5]{5\times 5 \times 5 \times 5 \times 5}\)

= 7.2\(\sqrt[5]{ 5^{5}}\)

= 7.2 × 5

= 36

\(7.2\sqrt[5]3125 \) = 36.

Now, try the simplifying radicals calculator to simplify the following radicals.

- \(4.4\times \sqrt[5] 800\)
- \(3\times \sqrt[3] {135}\)

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