Square root of 12 – Value, simplification and examples

This article will help you understand the value, simplification, and calculation of√12. Later, we will help you solve some real-life applications of √12 by using its value. So, let’s get started; we have a lot of things to share.

Definition of root 12

We know that we can find the square of a number by multiplying it twice with itself. Similarly, we can find the square root by inversing the operation of squaring. This means that 12 = a x a = a² and vice versa, a² = a x a = 12, where a is the quantity that represents the value of root 12. The mathematical representation of root 12 is given by √12 in radical form. It can also be written as 2√3.

Is root 12 a rational number?

If 12 is a perfect square, then the square root of 12 is also a rational number. But, we know that 12 is not a perfect square. Therefore, the value of √12 cannot be a rational number. This also means that the value of root 12 will be an infinite number that doesn’t terminate after the decimal point, and you won’t be able to write it in a fractional form.

So, √12 is an irrational number.

How to find the value of √12?

We can find the value of root 12 by prime factorization.

First, let us write the factors of 12,
12 = 2 x 2 x 3

For, √12, we can write these factors as
√12 = √(2 x 2 x 3) = √(2² x 3) = 2√3

Now, put the value of √3 = 1.732 so that we get
√12 = 2 x 1.732
√12 = 3.464
The value of √12 can be both positive and negative, but here in this article we will only consider the positive value of root 12.

The digits after the decimal point are never-ending, and they continue up to many places. The value of root 12 up to 10 decimal places is 3.4641016151

Table of square roots from 1 to 15

To make things easier for you, we are enlisting a table of square root values from 1 to 15. This table will come in handy while solving calculations and length problems.

Solved examples:

Question 1 – Find the value of 3√12 + 6√3
Solution –  Given, 3√12 + 6√3
We know that √12 = 3.464 and √3 = 1.732
Putting these values in the given equation,
= 3 x 3.464 + 6 x 1.732
= 10.392 + 10.392
= 20.784

Question 2 – Find the radius of a circle if its area is 12π cm²
Solution – Given, the area of the circle = 12π cm²
Now, area = πr² where, r is the radius of the circle.

So,
πr² = 12π cm²
We get, r² = 12 cm²
r = √12 cm²
Putting the value of √12 in the above equation,
We get, r = 3.464 cm

Therefore, the radius of the circle is 3.464 cm.

Question 3 – Simplify 3√12 + 2√3
Solution –  We have 3√12 + 2√3
Here, we can simplify √12 as 2√3
So, 3 (2√3) + 2√3
= 6 √3 + 2 √3
Taking √3 as a common from both terms,
We get (6+2) √3
So, the simplification of (3√12 + 2√3) gives 8√3