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Last updated on March 28th, 2025

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Square Root of 22500

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If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 22500.

Square Root of 22500 for US Students
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What is the Square Root of 22500?

The square root is the inverse of the square of the number. 22500 is a perfect square. The square root of 22500 is expressed in both radical and exponential form. In the radical form, it is expressed as √22500, whereas (22500)(1/2) in the exponential form. √22500 = 150, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

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Finding the Square Root of 22500

The prime factorization method is used for perfect square numbers. Let's learn the methods to find the square root:

 

  1. Prime factorization method
  2. Long division method
  3. Approximation method
Professor Greenline from BrightChamps

Square Root of 22500 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 22500 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 22500 Breaking it down, we get 2 x 2 x 3 x 3 x 5 x 5 x 5 x 5: 22 x 32 x 54

 

Step 2: Now we found out the prime factors of 22500. The second step is to make pairs of those prime factors. Since 22500 is a perfect square, the digits of the number can be grouped in pairs.

 

Therefore, calculating √22500 using prime factorization gives us 150.

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Square Root of 22500 by Long Division Method

The long division method is particularly used for both perfect and non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

 

Step 1: To begin with, we need to group the numbers from right to left. In the case of 22500, we need to group it as 00, 50, and 22.

 

Step 2: Now we need to find n whose square is less than or equal to 22. We can say n as '4' because 4 x 4 = 16, which is less than 22. Now the quotient is 4 after subtracting 22 - 16, the remainder is 6.

 

Step 3: Now let us bring down 50, which is the new dividend. Add the old divisor (4) with itself to get 8, which will be our new divisor.

 

Step 4: The new divisor will be 80. Now we find n such that 8n x n ≤ 650. Let us consider n as 8, now 88 x 8 = 704.

 

Step 5: Subtracting 650 from 704 gives a remainder of 54.

 

Step 6: Bring down the next pair, 00, to make it 5400. The new divisor becomes 800. Find n such that 800n x n ≤ 5400. Here, n is 6, so 806 x 6 = 4836.

 

Step 7: Subtracting 4836 from 5400 gives a remainder of 564.

 

Step 8: Continue this process until no remainder is left (or until you reach a satisfactory decimal precision). The result is 150.

Professor Greenline from BrightChamps

Square Root of 22500 by Approximation Method

The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 22500 using the approximation method.

 

Step 1: Now we have to find the closest perfect square of √22500. The smallest perfect square less than 22500 is 19600 (1402), and the largest perfect square greater than 22500 is 25600 (1602). √22500 falls exactly at 150.

 

Step 2: Since 22500 is a perfect square, there is no need for further approximation. The square root of 22500 is exactly 150.

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Common Mistakes and How to Avoid Them in the Square Root of 22500

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Square Root of 22500 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √22500?

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Explanation

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Problem 2

A square-shaped building measuring 22500 square feet is built; if each of the sides is √22500, what will be the square feet of half of the building?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √22500 x 5.

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Explanation

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (2025 + 2025)?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √22500 units and the width ‘w’ is 50 units.

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Explanation

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FAQ on Square Root of 22500

1.What is √22500 in its simplest form?

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2.Mention the factors of 22500.

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3.Calculate the square of 22500.

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4.Is 22500 a prime number?

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5.22500 is divisible by?

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

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7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 22500?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 22500?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 22500

  • Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: 122 = 144, and the square root of 144 is √144 = 12.

 

  • Rational number: A rational number is a number that can be expressed as a quotient or fraction p/q, where p and q are integers and q ≠ 0.

 

  • Perfect square: A perfect square is a number that is the square of an integer. Example: 22500 is a perfect square because it is 1502.

 

  • Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors. Example: 22500 = 22 x 32 x 54.

 

  • Long division method: The long division method is a technique used to find the square root of a number by dividing it into groups and finding the quotient step by step.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of 22500, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. Let’s make square roots an exciting part of every child’s math adventure!
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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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Max, the Girl Character from BrightChamps

Fun Fact

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

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