Square Root

# What Is the Square Root of 36? How to Find the Square Root of 36?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What Is the Square Root of 36? How to Find the Square Root of 36?

The square root of 36 is 6. The square root of a number is the value when multiplied by itself gives the original number. The square root for the exponential form is denoted as 36^{1/2} or 36^{0.5 }the radical way of writing 8 is expressed as √36. Thus, they give the original number when the number is squared.

The number 36 is a perfect square number that can be easily found. Since the square root of 36 is 6, where 6 is a rational number the square root of 36 can be found by three methods.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

**Methods to find the square root of 36**

There are three methods to find the square root of 36:

- Prime factorization method
- Long division method
- Repeated subtraction method

**Prime factorization method**

Prime factorization to find the square root is used to find only those numbers that are perfect squares. n is the prime factor. When the prime factors of the number are found the similar factors are squared as n^{2}. After taking a square on both sides the root with a square is canceled.

**Step 1:**Find the prime factors of the given number- Prime factors of 36 = 2 x 2 x 3 x 3

**Step 2:**Take the similar factors, by multiplying them we get the square root- 36 = 2 x 3 = 6

The exponential form can be written as,

36 = 2^{2} x 3^{2}.

Next, take square on both sides

√36 = √2^{2}x √3^{2}

√36 = 2 x 3 = 6

Hence, the square root of √**36 = 6.**

**Long division method**

Finding the square root of a perfect square number using the long division method is simple. Since 36 is a small two-digit number the divisor itself is a small single-digit number that can be its square.

Hence, √**36 = 6**.

**Repeated subtraction method**

The repeated subtraction method first subtracts the given number from the odd numbers until you get zero. The step in which zero is obtained is the square root of the number. It is a time-consuming and lengthy process.

- 36-1 = 35
- 35-3 = 32
- 32-5 = 27
- 27-7 = 20
- 20-9 = 11
- 11-11 = 0

We got zero in the sixth step. Hence, √**36 = 6**.

**Solved examples:**

**Q1: what is the value of 4 when multiplied by 36**

A1: The square root of 36 = 6

Therefore, by multiplying 4×6 =24

Hence the value of 4 when multiplied by 36 = 24.

**Q2: what is the area of the square whose each side is equal to 6cm**

A2: Area of the square = x^{2}

Here x= 6

Therefore, 6^{2} = 6 x 6 = 36

Hence the area of the square with 6cm = 36 sq. cm

**Q3: Find the perimeter of the square if the area of the square tile is 36.**

A3: The area of the square = 36.

The side length of the tile = √area

Therefore, √36 = 6

A square has 4 sides, by multiplying we get 24.

Therefore the perimeter of the tile = 24 units

**Q4: Find the square root of 36 using the law of exponential.**

A4: The square root for exponential is replaced by** 36 ^{1/2}**

= (6

^{2})

^{1/2}

Therefore, 6

^{2}= 36= [6 (a

^{m})

^{n}. =a

^{mn}]

√36 = 6

**Q5: What is the square root of 36 using the prime factor**

A5: 36 = 2 x 2 x 3 x 3

36 = 2 x 3 = 6

√36 = 6

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

**Frequently asked questions**

**What is the square root of 36?**

The √36 = 6

**Is 36 a perfect square number?**

Yes, 36 is a perfect square number.

**What is a rational number?**

A rational number is a real number where the denominator when divided is, pq ≠ 0.

**What is the square root of 5?**

The square root of 5 = 2.23

**What is the square root of 36 using the long division method?**

√ 36 = 6

**What are the methods to find the square root of rational numbers?**

There are three methods to find the square root of 36

Prime factorization method

Long division method

Repeated subtraction method

We hope that we have answered all your queries related to the square root of 36!

Written by by

Prerit Jain