The square root of 150 is 12.247. Before we start how to compute the square root of 150, let us note down few interesting facts about the number 150.

**•** 150 is a composite even number.

**•** 150 is the sum of eight consecutive primes from 7 to 31, that is, 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 = 150.

**Also Read:** Properties of square roots

**Important Things:**

**√150 = 12.247**- 150 is not a perfect square.
**150**is the exponential form of square root of 150.^{1/2}**√150**is the radical form of square root of 150.- The square root of 150 is 12.247 corrected up to 3 decimal places.
- Square of
**150: 150×150 = 22500** **√150**is a quadratic surd.- The simplified form of
**√150**is**5√6**.

Let us now calculate the square root of 150.

**Simplify square root of 150?**

Let us now find the simplest radical form of the square root of 150. We will write 150 as the product of a perfect square and a non-perfect square. Note that

150=25×6.

Here 25 is a perfect square number whose square root is 5. We will take square root on both sides of 150=25×6. Doing that we get

$\sqrt{150}=\sqrt{25 \times 6}$

$=\sqrt{25} \times \sqrt{6}$ $[\because \sqrt{a \times b}=\sqrt{a} \times \sqrt{b}]$

$=5 \times \sqrt{6}=5\sqrt{6}$

So the simplest form of the square root of 150 is 5√6.

**What is the value of root 150?**

We have computed that the square root of 150 is 5√6. Using the fact √6=2.4494, we get that

√150 = 5√6 = 5 × 2.4494 = 12.247

So 12.247 is the value of the square root of 150.

**Square root of 150 by Prime Factorization**

To find the square root of 150 by the prime factorization method, we will first need to factorize the number 150.

As 150 is an even number, 2 will divide it. Thus we get

150=2×75.

Next, we will factorize 75. As the sum of digits of 75, that is, 7+5=12 is divisible by 3, the number 75 will be divisible by 3. So we have

75=3×25

At last, 25=5×5.

So the prime factorization of 150 is

150=2×3×5×5

Taking square root on both sides, we get that

$\sqrt{150}=\sqrt{2 \times 3 \times 5 \times 5}$

$=\sqrt{2 \times 3} \times \sqrt{5 \times 5}$ $[\because \sqrt{x \times y}=\sqrt{x} \times \sqrt{y}$ with $x=2 \times 3$ and $y=5 \times 5]$

$=\sqrt{6} \times 5$ $[\because \sqrt{a \times a}=a]$

$=5\sqrt{6}$

∴ the square root of 150 is 5√6.

**Is Square root of 150 Rational?**

From above we have √150=5√6. We all know that √6 is not a rational number. This implies that the square root of 150 is not a rational number. Note that √150 is a real number. Moreover, √150 is an irrational number.

**Is 150 a perfect square number?**

Since √150=5√6, we deduce that the square root of 150 is not a natural number. As a result, the number 150 is not a perfect square number. So its square root, that is, √150 is a quadratic surd.

**Conclusion:** 150 is a non-perfect square number.