How to Add and Subtract Radicals?

Radical Numbers are used to represent Square root of a number. For Example: 3 is the square root of number 9. We will represent it as √9 = 3. Here '√' is the radical symbol and number under radical symbol is called as radicand. We can perform arithmetic operations like addition, subtraction, multiplication etc. Let us see how to add and subtract Radicals:

Addition of radicals: For addition of radicals we have to ensure that number under radical should be equal; if it is not equal then we will make it equal. Let us take example to understand it.

Assume that we want to add √3 and 4√3. Here numbers under radical sign are equal so we can add them like simple arithmetic numbers:

√3 + 4√3 = 5√3,

Now we will see subtraction of radicals. Say we want to subtract 3√2 from 6√2. Here radicands of both numbers are equal so we can perform subtraction as:

6√2 - 3√2 = 3√2.

If radicands are different in both numbers then make them same.

Now let us take another example to better understand this concept. Assume that we have to subtract √12 from √27. Here numbers under radical are not equal so we cannot add them. We have to make radicands equal. So we can write √12 as √2 * 2 * 3 and we can write √27 as √3 * 3 * 3. Now radicals are:

3√3 - 2√3,

Here radicands of both numbers are equal, so we can add them as:

3√3 - 2√3 = 1√3.

Just like addition, subtraction follows same property that radicands of both numbers should be same.