The square root of 36 is a number when we multiply by itself, it will be 36. Note that if a square has an area of 36 unit^{2}, then we use the value of the square root of 36 to find the length of the square. We denote the square root of 36 by the symbol √36. In this section, we will learn how to determine the value of √36.

**The value of the square root of 36 is 6**.

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**Important Things about Root 36:**

**36**is a perfect square.**√36 = 6****36**is the exponential form of square root of^{1/2}**36**.**√36**is the radical form of square root of**36**.- The square root of
**36**is**6.000**in decimal form. - Square of
**36: 36×36 = 1296**

Let us now calculate the square root of 36.

**What is the Square Root of 36?**

The square root of 36 is 6. To prove this, we will write 36 as a square of some numbers. Observe that 36 is a product of two numbers of 6‘s. So we have

36=6×6=6^{2}

Taking square root on both sides, we get that

√36 = √6^{2}

As square root can be written as power 1/2, we have

√36 = (6^{2})^{1/2} = 6^{2×}^{1/2} as we know that (a^{m})^{n }= a^{m×n}

= 6^{1 }= 6

So the value of the square root of 36 is 6.

**Is 36 a perfect square number?**

As we have calculated above that √36=6 and 6 is a whole number, we deduce that the square root of 36 is also a whole number. Now using the definition of a perfect square, we conclude that 36 is a perfect square number.

**Square root of 36 by Prime Factorization**

We will now find the square root of 36 by the prime factorization method. At first, we have to factorize 36.

As 36 is an even number, 2 will divide it and we get

36=2×18.

Now we factorize the number 18. As 18 is an even number, we write

18=2×9.

Lastly, as 9=3×3 we finally get that

36 = 2×2×3×3 …(∗)

As 2 and 3 are prime numbers, we cannot factorize further.

So (∗) is the prime factorization of 36.

Taking square root on both sides of (∗), we get that

√36 = √(2×2×3×3)

= √(2×2) × √(3×3)

= 2×3 as we know that √a×a=a

= 6.

∴ the square root of 36 is 6.

**Is Square Root of 36 Rational?**

By definition, a rational number can be expressed as p/q where p and q are integers with q ≠ 0.

We have obtained that √36=6.

Note that 6=6/1.

So 6 can be written as p/q with p=6, q=1≠0. Thus 6 is a rational number.

Hence the square root of 36 is also a rational number.

**Conclusion:** √36 is not an irrational number.

#### Key Things about 36

- 36 is a composite even number.
- A square of length 6 unit has the area 36 unit
^{2}

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.