# Square root of 27

The square root of 27 is 5.196. Before we start how to compute the square root of 27, let us note down few interesting facts about the number 27.

27 is a composite odd number.

If a cube has a side of length 3 unit, then its volume will be 33=27. So 27 is a cube number.

Note that 27=3×9 and the sum of digits of 27 is = 2+7=9. The number 27 is the only positive integer which is 3 × sum of its digits.

The number 27 consists of the digits 2 and 7. Observe that the sum of the integers from 2 to 7, that is, 2+3+4+5+6+7 is equal to 27.

Let us now calculate the square root of 27.

#### Simplify square root of 27

What is the square root of 27 in simplest radical form? Note that 27=9×3. Observe that 9 is a perfect square number whose square root is 3. Taking square root on both sides of 27 = 9×3, we get that

$\sqrt{27}=\sqrt{9 \times 3}$

$=\sqrt{9} \times \sqrt{3}$  $[\because \sqrt{a \times b}=\sqrt{a} \times \sqrt{b}]$

$=3 \times \sqrt{3}=3\sqrt{3}$

So the simplest form of the square root of 27 is 3√3.

#### What is the value of root 27?

From above we get that the square root of 27 is 3√3. As we know that the value of √3 is 1.732, we obtain that

√27 = 3√3 = 3 × 1.732 = 5.196

So the value of the square root of 27 is 5.196

#### Square root of 27 by Prime Factorization

We will now find the square root of 27 by the prime factorization method. At first, we will factorize the number 27.

As the sum of digits of 27 is divisible by 3, we get that 3 will divide 27. So we write 27=3×9. Again as 9=3×3, we obtain that 27=3×9=3×3×3. Thus, the prime factorization of 27 is

$27=3 \times 3 \times 3$

We will take square root on both sides and doing that we get

$\sqrt{27}=\sqrt{3 \times 3 \times 3}$

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

$=3 \times \sqrt{3}$  $[\because \sqrt{a \times a}=a]$

$=3\sqrt{3}$

∴ $3\sqrt{3}$ is the square root of $27.$

#### Is Square root of 27 Rational?

We have computed that √27=3√3. It is known that √3 is an irrational number. So we deduce that the square root of 27 is an irrational number. In other words, √27 is not a rational number.

#### Is 27 a perfect square?

Since √27=3√3, we note that the square root of 27 is not a natural number. As a result, the number 27 is not a perfect square number. Thus, 27 is a non-perfect square number. So its square root, that is, √27 is a quadratic surd.

#### Important Things of Square Root of 27:

• √27 = 5.196
• 27 is not a perfect square.
• 271/2 is the exponential form of square root of 27.
• √27 is the radical form of square root of 27.
• The square root of 27 is 5.196 corrected up to 3 decimal places.
• Square of 27: 27×27 = 729
• √27 is a quadratic surd.
• The simplified form of √27 is 3√3.