Adding Square Roots - A Comprehensive Guide

Solving square roots doesn’t only mean factorizing the number and making pair of twos. But you can also perform basic mathematical operations on this type of integer. One of the most common and simplest tasks is adding square roots.

Performing the addition of square roots is not a difficult task if you know some basic steps. Aren’t you familiar with them? You should read this guide about adding square roots till the end. In this blog, we will share a step-by-step guide as well as a solved example for better understanding.

What is a Square Root?

A square root is the factor of a number that gives the original number when multiplied by itself. Using this, a student can find a pair of the same numbers that can exactly divide the given number. Mathematically, it is also called the inverse of the square of any particular number.

For example, the square root of “4” is “2” because when “4” is divided by “2”, it gives another “2” as the answer that satisfies the definition of square root. Similarly, we can find the square root of any number by inversing the squaring process.

A square root is represented by putting the symbol “√” above the number. This symbol is called Radical while the number inside this symbol is called Radicand.

A brief guide on adding square roots

Normally, we get the addition problems in simple integer format. It means we are mostly asked to add numbers instead of fractions. In Mathematics, you will also find problems when you have to add square roots. It is a bit similar to adding integers but it also includes some additional sections.

For solving problems of adding with square roots, the following conditions must be fulfilled.

  • The radicands of all terms should be the same
  • Every term should have a radical sign. A simple number can’t be added in a square root / radical term.

If you have terms that are fulfilling the above conditions, you can add and subtract them easily. You can also make the radicand the same through factorization. It means that you have to factorize/divide the original number given as a radicand. Here are some steps that you have to follow for adding square roots.

  • Check if the radicands are the same.
  • If not, factorize the numbers to make them same under the radical sign.
  • When you have all terms with the same radicands, you only have to add the numbers given on the left side of every radical sign.
  • If there is no specific number shown there, it will be taken as “1”.
  • After addition, you only have to write the sum of all numbers beside the radical sign and the other portion as it is.

Simply follow these steps to add all square roots and get a single term. If you are still confused and unable to understand the process, you can take help by adding square roots calculator.

This online maths calculator can help you in finding the addition of square roots with the same radicands as well as different radicands. It means that you don’t have to get the same radicands manually but the calculator will do it automatically. Along with this, you can add square roots using this tool and complete your assignments quickly.

Solved example of adding square roots

We aim to explain the process of adding square roots to our readers to let them better understand the process. That’s why, we have solved an example related to this problem here.

Example 1:

Add the following square roots: 2√6 ,9√24 , √36 , 3√6 .


We can see that the numbers under the radical sign are not the same. So, we first have to factorize them to get the same numbers as all radicands.

24 = 4 x 6

36 = 6 x 6

Now, we need to put them in the above terms and simplify them. Here are the final terms we have after the simplification.

9√24 = 18√6

√36 = 6√6

We can add all the terms as their radical has become “6”.

= 2√6 + 18√6 + 6√6 + 3√6

= 29√6

So, this is the final answer that we have got from the addition of square roots after the simplification of radicands.


By reading the above guide about adding square roots, we hope you have understood the method to add square roots. If you are unable to understand, you can use the adding square roots calculator in the beginning. Using this type of online tool will enable you to solve your questions and understand the solution because of its step-by-step solution.


Can you add square roots together?

Yes, we can add square roots together if their radicals are the same.

How do you add two roots?

We can add two roots by making their radicands the same. If the radicands are not identical, we can’t add or subtract them.

What are the rules for adding radicals?

There is a single rule for adding radicals and that is the identical radicands. If you have radicals with the same numbers under them, you can add them easily.

Do you add square roots when multiplying?

We don’t add square roots when multiplying. The square roots will be added only if the numbers inside the radicals are the same when multiplying.

How do you add radical examples?

We can add radical examples by making them “Like Radicals” if they are not.

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