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Last updated on May 26th, 2025

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Square Root of 13725

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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 13725.

Square Root of 13725 for Canadian Students
Professor Greenline from BrightChamps

What is the Square Root of 13725?

The square root is the inverse of the square of the number. 13725 is not a perfect square. The square root of 13725 is expressed in both radical and exponential form. In the radical form, it is expressed as √13725, whereas (13725)(1/2) in the exponential form. √13725 ≈ 117.1573, which is an irrational number because it cannot 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 13725

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 13725, methods such as the long division method and approximation method are used. Let us now learn these methods:

 

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

Square Root of 13725 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 13725 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 13725 Breaking it down, we get 3 × 3 × 5 × 5 × 61: 3² × 5² × 61

 

Step 2: Now we found out the prime factors of 13725. The next step is to make pairs of those prime factors. Since 13725 is not a perfect square, some digits of the number can’t be grouped in pairs.

 

Therefore, calculating the exact square root of 13725 using prime factorization is not possible, but it gives us a simplified radical form.

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Square Root of 13725 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we find the square root step-by-step. Let's learn how to find the square root using the long division method:

 

Step 1: Group the numbers from right to left. In the case of 13725, group it as 725 and 13.

 

Step 2: Find a number whose square is less than or equal to 13. Here, n is 3 because 3 × 3 = 9 ≤ 13. Subtracting 9 from 13 gives a remainder of 4.

 

Step 3: Bring down the next pair 25. The new dividend is 425.

 

Step 4: Double the divisor (3) to get 6, which will be part of our new divisor.

 

Step 5: Find a digit n such that 6n × n ≤ 425. Here, n is 7 because 67 × 7 = 469 > 425, but 66 × 6 = 396 < 425.

 

Step 6: Subtract 396 from 425 to get 29.

 

Step 7: Bring down pairs of zeros and repeat the process to find more decimal places. So, the square root of √13725 is approximately 117.1573.

Professor Greenline from BrightChamps

Square Root of 13725 by Approximation Method

The approximation method helps find the square roots easily by identifying the closest perfect squares. Let's find the square root of 13725 using this method:

 

Step 1: Identify the closest perfect squares to √13725. The smallest perfect square less than 13725 is 13689 (117²) and the largest perfect square greater than 13725 is 13824 (118²). √13725 falls between 117 and 118.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (13725 - 13689) / (13824 - 13689) ≈ 0.36

 

Add this decimal to the smaller square root: 117 + 0.36 = 117.36. So, the square root of 13725 is approximately 117.36.

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Common Mistakes and How to Avoid Them in the Square Root of 13725

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.

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 often use only the positive square root in practical applications. For example, √50 = 7.07, but there is also -7.07, which should not be overlooked.

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Square Root of 13725 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 √147?

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The area of the square is 147 square units.

Explanation

The area of the square = side².

 

The side length is given as √147.

 

Area of the square = side² = √147 × √147 = 147.

 

Therefore, the area of the square box is 147 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 13725 square feet is built; if each of the sides is √13725, what will be the square feet of half of the building?

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6862.5 square feet

Explanation

Since the building is square-shaped, we can divide the given area by 2.

 

Dividing 13725 by 2 = 6862.5

 

So half of the building measures 6862.5 square feet.

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Problem 3

Calculate √13725 × 5.

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585.7865

Explanation

First, find the square root of 13725, which is approximately 117.1573.

 

Multiply 117.1573 by 5.

 

So 117.1573 × 5 = 585.7865

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (147 + 9)?

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The square root is 12.

Explanation

To find the square root, calculate the sum of (147 + 9). 147 + 9 = 156, and then √156 ≈ 12.49.

 

Therefore, the square root of (147 + 9) is approximately ±12.49.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √147 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is approximately 112.98 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

 

Perimeter = 2 × (√147 + 38) ≈ 2 × (12.124 + 38) = 2 × 50.124 = 100.248 units.

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FAQ on Square Root of 13725

1.What is √13725 in its simplest form?

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2.Mention the factors of 13725.

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3.Calculate the square of 13725.

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4.Is 13725 a prime number?

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5.13725 is divisible by?

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

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7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 13725?

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8.How do technology and digital tools in Canada support learning Algebra and Square Root of 13725?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 13725

  • Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse is √16 = 4.

 

  • Irrational number: An irrational number cannot be expressed as a fraction of two integers. Example: √2, π.

 

  • Principal square root: The non-negative square root of a number is known as the principal square root.

 

  • Prime factorization: Expressing a number as a product of its prime factors. Example: The prime factorization of 18 is 2 × 3².

 

  • Long division method: A method used to find the square root of a number by dividing it into smaller, manageable parts. It is particularly useful for non-perfect squares.
Professor Greenline from BrightChamps

About BrightChamps in Canada

At BrightChamps, we know algebra is more than just symbols—it’s a key to open many doors! Our aim is to support kids across Canada in grasping important math skills, such as today’s focus on the Square Root of 13725, highlighting square roots in a fun, engaging, and easy-to-understand way. Whether your child is measuring how fast a roller coaster moves at Canada’s Wonderland, tracking hockey scores, or planning their allowance for the latest gadgets, mastering algebra helps build their confidence for daily tasks. Our hands-on lessons make learning enjoyable and straightforward. Since kids in Canada learn in diverse ways, we tailor lessons to their individual style. From Toronto’s busy streets to British Columbia’s stunning landscapes, BrightChamps brings math to life across Canada. Let’s make square roots a fun part of your child’s math experience!
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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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