# Radical Calculator

Radical Calculator is used to determine the simplified radical expression when we are given certain values. The radical of a number is also the root (square root, cube root, or n^{th} root) of that number.

## What is a Radical Calculator?

Radical Calculator is a free online tool that is used to simplify the given radical expression with the aim of completely removing the radical sign if possible. An algebraic expression that consists of radicals is known as a radical expression. To use the * radical calculator*, enter the values in the input boxes.

### Radical Calculator

NOTE: Value of 'n' should be greater than or equal to 2. Enter the values up to 3 digits only.

## How to Use the Radical Calculator?

Please follow the steps given below to find the simplified radical expression using the online radical calculator:

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

## How Does Radical Calculator Work?

To simplify a radical expression we have to reduce the n^{th} root to its simplified form. Suppose our radical is of the form a ⁿ√x. Here, "a" is known as the constant, "n" is used to signify the n^{th} root and "x" is the radicand or the expression under the radical sign. The steps given below are followed in order to simplify a radical expression:

**Step 1:**We first consider the number under the radical sign. Thus, we will first simplify ⁿ√x.**Step 2:**We will express x as a product of its prime factors.**Step 3:**As we have to reduce the n^{th}root hence, we start grouping the prime factors that have the same value in powers of n.**Step 4:**Now the factors that are raised to the n^{th}power can be written outside the radical sign. Once shifted, we remove the corresponding exponent.**Step 5:**Multiply "a" with all the factors outside the radical sign.**Step 6:**Multiply all remaining terms under the radical sign to get the simplified radical expression. If there are no terms under the radical sign, it implies that the radical sign has been eliminated.

## Solved Examples On Radicals

**Example 1: **Simplify \(4\sqrt[3]{135}\) and verify it using the online radical calculator.

**Solution:**

Writing the radicand as a product of its prime factors we get

\(4\sqrt[3]{135}\) = 4 × \(\sqrt[3]{3\times 3\times 3\times 5}\)

= 4 × \(\sqrt[3]{3^{3}\times 5}\)

= 4 × 3 × \(\sqrt[3]{ 5}\)

= 12\(\sqrt[3]{ 5}\)

Thus, \(4\sqrt[3]{135}\) can be reduced to 12\(\sqrt[3]{ 5}\).

**Example 2: **Simplify \(1.2\sqrt[2]{144}\) and verify it using the online radical calculator.

**Solution:**

Writing the radicand as a product of its prime factors we get

\(1.2\sqrt[2]{144}\) = \(1.2\sqrt[2]{2\times 2\times 2\times 2\times 3\times 3}\)

= \(1.2\sqrt[2]{2^{2}\times 2^{2} \times3^{2}}\)

= 1.2 × 2 × 2 × 3

= 14.4

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

- \(5\sqrt[3]{343}\)
- \(3.2\sqrt[4]{768}\)

**☛ Math Calculators:**

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