Square Root

# What Is the Square Root of 9? | How To Find the Square Root of 9?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What Is the Square Root of 9? | How To Find the Square Root of 9?

The square root of 9 is 3. The square root of any number is just the inversion of squaring the given number. The number when multiplied twice gives the original value. For the given number 9, when the number 3 is squared 3^{2} or when multiplied twice by 3*3 we get 9.

For a perfect square number like 9 finding the square root of the number is simple as they are whole numbers and not integers. Long division is used to find the square root of irrational and non-perfect square numbers. Since 9 can be the ratio of two numbers it is a rational number p/q, q = 0.

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**How to find square root of 9?**

There are three methods that are used to find the square root of a number that has perfect squares(here the number is 9).

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

**Long division method**

Finding the divisor for the long division method is much simpler than those that are imperfect squares. When 3 is multiplied twice it gives 9 hence, the number 3 is used as a divisor.

Hence, **9**** = 3.**

**Repeated subtraction method**

Using the repeated subtraction method, the square root of the number can be easily solved but consumes time. Hence, the prime factorization and the long division method are widely used to find the square root of the number. Start subtracting the given number by the first odd number, take the given value, and further subtract the number with the next odd number repeat the step until you reach zero.

- 9-1 = 8
- 8-3 = 5
- 5-5 = 0

Here the number zero is obtained in the third step.

Hence, **√9 = 3.**

**Prime factorization method**

Prime factorization is one of the simplest methods used to find the square root of a given number. Take the prime factor of the number as n square the given number we get n^{2}, take a single value, and multiply with the other square. By doing so we will get the square root of the number.

Prime factor of 9 = 3×3

The common factor is only 3^{2} and they are the squares of the given number

Hence, **√9 = 3.**

**Solved examples**

**Example 1: What is the sum of the square of 9 and the square root of 9?**

Square of 9= 81

The square root of **√**9 = 3

The sum of the square of 9 and the square root of 9 = 81+3 = 84

**Example 2: Joe wants to find the square root value of 4/9 to **help him solve the sum

The √9 = 3.

The √4 = 2

Therefore, **√**4/9 = 2/3.

**Example 3: Solve √9 + 10 √9**

The

**√**9 = 3.

Hence, 3 + 10 (3).

= 3+30

=33.

**Example 4: what is the area of the square whose each side is equal to 3cm**

Area of the square = x2

Here x= 3

Therefore, 32 = 3 3 = 9

Hence the area of the square with 3cm = 9 sq. cm

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**Frequently asked questions**

**What is the square root of 9?**

The square root of 9 = 3.

**Explain why the square root of 9 is a rational number.**

When finding the prime factor of 9 we get 3^{2} which is entirely an even power and hence all the numbers are positive integers which makes them rational numbers.

**What is the value of 9 and the square root of 9**?

The square root of 9 is 3, therefore 9**√**9 = 9*3 = 27

**What is the real value for the square root of 9**?

The actual value for the **√**9 = 3

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

The square root of 5 = 2.23

**What is the square root of (-9)?**

The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root.

**Is 9 a perfect square number?**

Yes, 9 is a perfect square number.

Written by

Prerit Jain