Adding Radicals Calculator

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

What is Adding Radicals Calculator?

'Cuemath's Adding Radicals Calculator' is an online tool that helps to calculate the sum of the given two radicals expressions. Cuemath's online Adding Radicals Calculator helps you to calculate the sum of the given two radicals expressions in a few seconds.

How to Use the Adding Radicals Calculator?

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

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

How to Add 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, add both the values.

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

Solved Example:

Add 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.

\(\sqrt[3] 80= \sqrt [3]{2 \times 2 \times 2 \times 2 \times 5} =2\sqrt[3]{2 \times 5} = 2\sqrt[3]10 = 4.309\)

\(4\sqrt[4] 96= 4\sqrt [4]{2 \times 2 \times 2 \times 2 \times 2 \times 3} =4×2\sqrt[4]{2 \times 3} = 8\sqrt[4]6 = 12.521\)  

Add the following radicals \(\sqrt[3] 80 + 4\sqrt[4] 96\) = 4.309 + 12.521 = 16.83

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

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