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Last updated on December 2nd, 2024

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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 Thai 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

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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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Explanation

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Problem 2

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

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Explanation

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Problem 3

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

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Explanation

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Problem 4

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

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Explanation

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Problem 5

Find (√9 / √49) × (√36/√64)

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Explanation

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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 Thailand make better decisions in daily life?

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

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

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

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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 Thailand

At BrightChamps, we understand algebra is more than just symbols—it opens up a world of opportunities! Our mission is to help children across Thailand develop essential math skills, focusing today on the Square Root of 9 with a special look at square roots—in a lively, enjoyable, and easy-to-follow manner. Whether your child is discovering the speed of a roller coaster at Dream World, tallying local football scores, or managing their allowance to buy the latest gadgets, mastering algebra gives them confidence for everyday life. Our interactive lessons make learning fun and straightforward. Since children in Thailand have varied learning styles, we personalize our approach for each child. From Bangkok’s busy streets to Phuket’s tropical islands, BrightChamps brings math to life, making it relatable and exciting throughout Thailand. 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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