In this section, we will learn how to find the sum (or difference) of two or more surds.

Table of Contents

**How to add or subtract two or more surds**

The addition and subtraction of surds are the basic two operations on surds. The below steps need to be checked while adding two or more surds.

Step 1: First look into the sum (or difference) and check whether the surds involved in the sum (or difference) are in the simplest forms or not.

Step 2: If they are not in the simplest forms, then we have to convert them into their simplest forms.

Step 3: In this step, we will make two different lists of similar surds and dissimilar surds after making the simplest forms.

Step 4: Then we will add (or subtract) the rational coefficients of the similar surds and put the similar surd-factor beside this addition (or subtraction).

Step 5: The dissimilar surds will be connected with the desired $+$ or $-$ sign.

Step 6: The resultant surd will be the desired sum (or difference).

**Examples of addition of surds**

**Problem 1:** How to add two similar (or like) surds?

Solution: Lets consider two like surds $x\sqrt{a}$ and $y\sqrt{a}.$ Then their sum $=x\sqrt{a}+y\sqrt{a}$ $=(x+y)\sqrt{a}$

**Problem 2:** How to add two dissimilar (or unlike) surds?

Solution: Lets consider two unlike surds $x\sqrt{a}$ and $y\sqrt{b}$ where $a$ and $b$ are two different rational numbers. Then their sum is just $x\sqrt{a}+y\sqrt{b}.$ We cannot further simplify it.

**Examples of subtraction of surds**

**Problem 3:** How to subtract two like surds?

Solution: The subtraction of two similar surds $x\sqrt{a}$ and $y\sqrt{a}$ is $=x\sqrt{a}-y\sqrt{a}$ $(x-y)\sqrt{a}$

**Problem 4:** How to subtract two unlike surds?

Solution: The difference of two unlike surds $x\sqrt{a}$ and $y\sqrt{b}$ is $x\sqrt{a}-y\sqrt{b}.$ This cannot be further simplified.

Related Topics |