# Square root of 12

The square root of 12 is 3.464. It is denoted by the symbol √12. The simplified radical form of the square root of 12 is 2√3. In this section, we will learn about the square root of 12.

#### Key Things

• 12 is a composite even number.
• √12=3.464
• Square of 12: 12×12 = 144
• The radical form of square root of 12 is √12.
• The exponential form of square root of 12 is 121/2.
• Square root of 12 is 3.464 corrected up to 3 decimal places
• The simplest radical form of square root of 12 is 2√3.
• √12 is a
• 12 is not a perfect square number.
• Square root of 12 is not a rational number.

Let us now calculate the square root of 12.

#### Simplify square root of 12

What is the square root of 12 in simplest radical form? Note that

12=4×3.

Here 4 is a perfect square number whose square root is 2.

Taking square root on both sides of 12 = 4×3, we get that

√12 = √(4×3)

= √4 × √3  as we know that √(a×b)=√a × √b

= 2 × √3  as √4=2

= 2√3

So the simplest form of the square root of 12 is 2√3.

#### What is the value of root 12?

We have calculated above that the square root of 12 is 2√3.

As we know that √3=1.732, we obtain that

√12 = 2√3 = 2 × 1.732 = 3.464

∴ the value of the square root of 12 is 3.464

#### Square root of 12 by Prime Factorisation

We will use the prime factorisation method to find the square root of 12.

Firstly, we will factorise the number 12.

As 12 is an even number, it will be divisible by 2. So we write

12=2×6.

Now since 6=2×3, we obtain that 12=2×6=2×2×3. Thus,

12 = 2×2×3 …(∗)

is the prime factorization of 12 as both 2 and 3 are prime numbers.

We will take square root on both sides of (∗) and doing that we get

√12 = √(2×2×3)

= √(2×2) × √3  as we know that √(a×b)=√a×√b. Here a=2×2 and b=3.

= 2 × √3  as √(a×a)=a

= 2√3

So 2√3 is the value of the square root of 12.

#### Is Square root of 12 Rational?

From above we have that √12=2√3. It is known that √3 is an irrational number.

⇒ the square root of 12 is an irrational number.

In other words, √12 is not a rational number.

#### Is 12 a perfect square?

As √12=3√3, we deduce the square root of 12 is not a natural number.

⇒ the number 12 is not a perfect square number.

12 is a non-perfect square number.

Note that √12 is a quadratic surd.