Find Square Root of 36

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 unit², 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.

If you want to know more about square roots, visit the following pages:

• Basic concepts of square roots
• Properties of square roots

Important Things about Root 36:

• 36 is a perfect square.
• √36 = 6
• 36^1/2 is the exponential form of square root of 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=6²

Taking square root on both sides, we get that

√36 = √6²

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

√36 = (6²)^1/2 = 6^2×1/2   as we know that (a^m)ⁿ = a^m×n

= 6¹ = 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 unit²