Dividing Radicals Calculator

A radical expression is defined as an expression that contains an expression with the radical symbol (√).

What is the Dividing Radicals Calculator?

'Dividing Radicals Calculator' is an online tool that helps to calculate the division of the given two radicals expressions. Online Dividing Radicals Calculator helps you to calculate the division of the given two radicals expressions in a few seconds.

How to Use the Dividing Radicals Calculator?

Please follow the steps below on how to use the calculator:

• Step 1: Enter the value of a, x, and n values in the given input boxes for the radical expression a ⁿ√x
• Step 2: Enter the value of a₁, x₁, and n₁ values in the given input boxes for the radical expression a₁ ⁿ₁√x₁.
• Step 3: Click on "Divide" to find the division of the given two radicals expressions
• Step 4: Click on "Reset" to clear the fields and enter the new values.

How to Divide Radicals?

The following steps would help in simplifying radicals:

• Step1: Write the number within the radical as the product of its prime factors.
• Step2: Based on the root of the radical take one factor out for n similar radicals within the radical.
• Step3: Find the product of the numbers outside the radical and the product of the numbers within the radical and write them together.
• Step4: After simplifying both the radicals, divide both the values.

Let us try to understand the simplification of radicals with the help of an example.

Solved Example:

Divide the radicals \(\sqrt[3] 80\) and \(4\sqrt[4] 96\)

Solution:  

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

\(\sqrt[3] 80= \sqrt [3]{2 \times 2 \times 2 \times 2 \times 5} =2\sqrt[3]{2 \times 5} = 2\sqrt[3]10 = 4.3088\)

\(4\sqrt[4] 96= 4\sqrt [4]{2 \times 2 \times 2 \times 2 \times 2 \times 3} =4×2\sqrt[4]{2 \times 3} = 8\sqrt[4]6 = 12.520\)  

Divide the following radicals \(\sqrt[3] 80 ÷ 4\sqrt[4] 96\) = 2.154 ÷ 12.0520 = 0.344

Similarly, you can try the calculator to divide the following radical expressions:

• \(4\times \sqrt[5] 800\) and \(3\times \sqrt[3] {135}\)
• \(2\times \sqrt[4] {64}\) and \(5\times \sqrt[5] {625}\)