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Last updated on May 26th, 2025

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Square Root of 9

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The square root of 9 is a value “y” such that when “y” is multiplied by itself → y × y, the result is 9. The number 9 has a unique non-negative square root, called the principal square root. Square root concept are applied in real life in the field of engineering, GPS and distance calculations, for scaling objects proportionally, etc.

Square Root of 9 for Indian Students
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What Is the Square Root of 9?

The square root of 9 is ±3, where 3 is the positive solution of the equation x2 = 9. Finding the square root is just the inverse of squaring a number and hence, squaring 3 will result in 9. The square root of 9 is written as √9 in radical form, where the ‘√’  sign is called the “radical” sign. In exponential form, it is written as (9)1/2 
 

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Finding the Square Root of 9

We can find the square root of 9 through various methods. They are:

 

  • Prime factorization method

 

  • Long division method

 

  • Repeated subtraction method
     
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Square Root of 9 By Prime Factorization Method

The prime factorization of 9 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore.

 

  • Find the prime factors of 9.

 

  • After factorizing 9, make pairs out of the factors to get the square root.

 

  •  If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs.

 

So, Prime factorization of 9 = 3 ×3 

Square root of 9= √[3 × 3] = 3

 

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Square Root of 9 By Long Division Method

This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.


Follow the steps to calculate the square root of 9:
Step 1: Write the number 9 and draw a bar above the pair of digits from right to left.

Step 2: Now, find the greatest number whose square is less than or equal to 9. Here, it is 3 because 32=9


Step 3: now divide 9 by 3 (the number we got from Step 2) such that we get 3 as a quotient, and we get a remainder 0. 
 
Step 4: The quotient obtained is the square root of 9. In this case, it is 3.

 

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Square Root of 9 By Subtraction Method

We know that the sum of the first n odd numbers is n2. We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:


Step 1: take the number 9 and then subtract the first odd number from it. Here, in this case, it is 9-1=8


Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 8, and again subtract the next odd number after 1, which is 3, → 8-3=5.


Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 3 steps.


So, the square root is equal to the count, i.e., the square root of 9 is ±3.

 

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Common Mistakes and How to Avoid Them in the Square Root of 9

When we find the square root of 4, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.

Mistake 1

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Incorrectly applying the square root property

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Square root do not distribute over additions. For example, √9 ≠   √4+√5
 

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Square Root of 9 Examples

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Problem 1

Find √(4×9)×√(4×9)×√(4×9) ?

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 √(4×9)×√(4×9)×√(4×9)

 

= (4×9)×√(4×9)

 

=  (4×9)×2×3

 

=216


Answer : 216
 

Explanation

We found the values of the square roots of 4 and 9, then simplified the expression using square root concepts and multiplied the values.
 

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Problem 2

What is √9 multiplied by 45 and then divided by 5 ?

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√9 × 45/5

 

= 3×9

 

= 27


Answer: 27 
 

Explanation

finding the value of √9 and multiplying by 45/5.
 

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Problem 3

A circular dish of radius equals to 3 meters. Find its area.

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radius = 3 m


Area of a circle = π×(radius)2


⇒ Area of a circle = 3.14×(3)2


 ⇒ Area of a circle=3.14×9 = 28.26 sq. meters


Answer: The area of a circular dish is 28.26 sq. meters
 

Explanation

Applying the formula for finding the area of a circle with a given radius.

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Problem 4

Find the length of a side of a square whose area is 9 cm²

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Given, the area = 9 cm2


We know that, (side of a square)2 = area of square


Or,  (side of a square)2 = 9


Or,  (side of a square)= √9


Or, the side of a square = ± 3.


But, the length of a square is a positive quantity only, so, the length of the side is 3 cm.


Answer: 3 cm

Explanation

We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its square root is the measure of the side of the square
 

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Problem 5

Find (√9 / √49) × (√36/√64)

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(√9 / √49) × (√36/√64)

 

=(3/7)×(6/8)  

 

= 9/28


Answer : 9/28 
 

Explanation

we firstly found out the values of √9, √49,√36 and √64 then solved .

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FAQs on 9 Square Root

1.What is the square of 9 ?

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2.What is the value of √5?

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3.Is 9 a perfect square or non-perfect square?

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4.Is the square root of 9 a rational or irrational number?

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5.How to solve √10?

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6.How does learning Algebra help students in India make better decisions in daily life?

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7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 9?

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8.How do technology and digital tools in India support learning Algebra and Square Root of 9?

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9.Does learning Algebra support future career opportunities for students in India?

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Important Glossaries for Square Root of 9

  • Exponential form:  An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 24 = 16, where 2 is the base, 4 is the exponent 

 

  • Prime Factorization:  Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3

 

  • Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

 

  • Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

 

  • Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 2
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About BrightChamps in India

At BrightChamps, we see algebra as more than just symbols—it opens doors to endless opportunities! Our mission is to help children all over India develop vital math skills, focusing today on the Square Root of 9 with special attention to understanding square roots—in a way that’s engaging, lively, and easy to follow. Whether your child is calculating the speed of a passing train, keeping scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra gives them the confidence needed for everyday situations. Our interactive lessons keep learning simple and fun. As kids in India have varied learning styles, we personalize our approach to match each child. From the busy markets of Mumbai to Delhi’s vibrant streets, BrightChamps brings math to life, making it relatable and exciting throughout India. Let’s make square roots a joyful part of every child’s math journey!
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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