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Last updated on May 26th, 2025

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Square Root of 525

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If a number is multiplied by itself, the result is a square. The inverse operation of squaring a number is finding its square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 525.

Square Root of 525 for US Students
Professor Greenline from BrightChamps

What is the Square Root of 525?

The square root is the inverse of squaring a number. 525 is not a perfect square. The square root of 525 can be expressed in both radical and exponential forms. In radical form, it is expressed as √525, whereas in exponential form, it is (525)(1/2). √525 ≈ 22.91288, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

Professor Greenline from BrightChamps

Finding the Square Root of 525

The prime factorization method is used for perfect squares. However, for non-perfect squares, methods like the long division method and approximation method are used. Let us explore these methods: -

 

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

Square Root of 525 by Prime Factorization Method

Prime factorization involves expressing a number as a product of its prime factors. Let us break down 525 into its prime factors:

 

Step 1: Find the prime factors of 525 Breaking it down, we get 3 × 5 × 5 × 7: 31 × 52 × 71

 

Step 2: Since 525 is not a perfect square, the digits cannot be grouped into pairs.

 

Therefore, calculating the square root of 525 using prime factorization alone is not feasible.

Professor Greenline from BrightChamps

Square Root of 525 by Long Division Method

The long division method is useful for finding the square root of non-perfect squares. Let's find the square root of 525 using this method, step by step:

 

Step 1: Group the digits of 525 from right to left as 25 and 5.

 

Step 2: Find the largest integer n whose square is less than or equal to 5. Here, n is 2 because 2 × 2 = 4. The remainder is 1.

 

Step 3: Bring down the next pair, 25, making the new dividend 125. Add the previous divisor to itself to get 4, making the new divisor.

 

Step 4: Determine n such that 4n × n ≤ 125. If n is 2, then 42 × 2 = 84.

 

Step 5: Subtract 84 from 125, giving a remainder of 41. The quotient so far is 22. Step 6: Bring down two zeros, making the new dividend 4100.

 

Step 7: Find the new divisor, which is 229, because 229 × 9 = 2061.

 

Step 8: Subtract 2061 from 4100, giving a remainder of 2039.

 

Step 9: The quotient so far is 22.9. Repeat these steps until you have sufficient decimal places.

 

Thus, √525 ≈ 22.91.

Professor Greenline from BrightChamps

Square Root of 525 by Approximation Method

The approximation method is another approach to find square roots. Let's approximate the square root of 525:

 

Step 1: Identify the perfect squares closest to 525. 484 and 529 are the nearest perfect squares, with square roots 22 and 23, respectively.

 

Step 2: Apply the formula:

 

(Given number - smaller perfect square) / (Larger perfect square - smaller perfect square)

 

(525 - 484) / (529 - 484) = 41 / 45 ≈ 0.9111

 

Add this decimal to the smaller root: 22 + 0.9111 = 22.9111

 

Therefore, √525 ≈ 22.9111.

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Common Mistakes and How to Avoid Them in the Square Root of 525

Mistakes are common when calculating square roots, such as forgetting negative roots or misapplying methods. Let's examine some common errors and how to avoid them.

Mistake 1

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Forgetting about the negative square root

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It's important to remember that numbers have both positive and negative square roots. However, we typically focus on the positive square root for practical applications. For example, √64 = 8, but there is also -8.

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Square Root of 525 Examples

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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 √525?

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The area of the square is 525 square units.

Explanation

The area of a square = side².

 

The side length is given as √525.

 

Area = (√525)² = 525.

 

Therefore, the area of the square box is 525 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 525 square feet is built; if each side is √525, what will be the square feet of half of the building?

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262.5 square feet

Explanation

Divide the total area by 2 for half of the building: 525 / 2 = 262.5

 

So half of the building measures 262.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √525 × 5.

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114.56

Explanation

First, find the square root of 525, which is approximately 22.91288.

 

Then multiply 22.91288 by 5:

 

22.91288 × 5 ≈ 114.56

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (525 + 100)?

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The square root is approximately 25.

Explanation

First, find the sum of (525 + 100): 525 + 100 = 625.

 

Then find the square root: √625 = 25.

 

Therefore, the square root of (525 + 100) is ±25.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √525 units and the width ‘w’ is 50 units.

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The perimeter of the rectangle is approximately 145.83 units.

Explanation

Perimeter of a rectangle = 2 × (length + width).

 

Perimeter = 2 × (√525 + 50)

 

= 2 × (22.91288 + 50) ≈ 145.83 units.

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FAQ on Square Root of 525

1.What is √525 in its simplest form?

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2.Mention the factors of 525.

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3.Calculate the square of 525.

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4.Is 525 a prime number?

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5.525 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 525?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 525?

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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 525

  • Square root: The square root is the inverse of squaring a number. For example, 42 = 16, so the square root is √16 = 4.

 

  • Irrational number: An irrational number cannot be expressed as a fraction of two integers, with a non-zero denominator. √525 is an example.

 

  • Principal square root: The positive square root, often used in practical applications, is known as the principal square root. For example, the principal square root of 16 is 4.

 

  • Prime factorization: This is the expression of a number as a product of its prime factors. For example, the prime factorization of 525 is 3 × 52 × 7.

 

  • Long division method: A method for finding square roots of non-perfect squares by dividing in steps, offering a precise decimal value.
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 525, 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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Fun Fact

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

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