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Last updated on May 26th, 2025

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Square Root of 15129

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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 15129.

Square Root of 15129 for Thai Students
Professor Greenline from BrightChamps

What is the Square Root of 15129?

The square root is the inverse of the square of a number. 15129 is a perfect square. The square root of 15129 is expressed in both radical and exponential forms. In the radical form, it is expressed as √15129, whereas 15129(1/2) is the exponential form. √15129 = 123, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 15129

The prime factorization method is used for perfect square numbers. The long division method and approximation method can also be applied. Let us now learn the following methods: -

 

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

Square Root of 15129 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Here is how 15129 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 15129. By inspection or trial division, we find that 15129 = 123 × 123. Thus, the prime factorization is 32 × 412

 

Step 2: Since 15129 is a perfect square, the digits of the number can be grouped into pairs: (3 × 41) × (3 × 41).

 

Hence, calculating the square root of 15129 using prime factorization gives us 123.

Professor Greenline from BrightChamps

Square Root of 15129 by Long Division Method

The long division method can also be used for non-perfect square numbers, but let's apply it to 15129 for illustration:

 

Step 1: Start by grouping the digits from right to left. For 15129, group as 15 | 129.

 

Step 2: Find the largest number whose square is less than or equal to 15. This number is 3, because 3 × 3 = 9.

 

Step 3: Subtract 9 from 15 to get a remainder of 6. Bring down the next pair of digits, 29, to get the new dividend 629.

 

Step 4: Double the quotient obtained so far (3) and write it as 6_.

 

Step 5: Find a digit n such that 6n × n is less than or equal to 629. The digit is 3, because 63 × 3 = 189.

 

Step 6: Subtract 189 from 629 to get 440. Bring down the next pair of zeros to get 4400.

 

Step 7: Continue the process. The whole number part of the quotient is the square root. Through this method, we find that the square root of 15129 is 123.

Professor Greenline from BrightChamps

Square Root of 15129 by Approximation Method

The approximation method involves finding the closest perfect squares. Since 15129 is a perfect square, this method is straightforward:

 

Step 1: Identify the closest perfect squares around 15129.

 

Step 2: Since 15129 is a perfect square, we already know its square root is exactly 123.

 

Step 3: If it were not a perfect square, you would use the formula (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) for a more refined approximation.

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Common Mistakes and How to Avoid Them in the Square Root of 15129

Students make mistakes while finding square roots, such as forgetting negative square roots or skipping the long division method. Here are some common mistakes students make and how to avoid them.

Mistake 1

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Forgetting about the Negative Square Root

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It is important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root as it is more commonly used. For example, √25 = 5, but there is also -5.

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Square Root of 15129 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 √15129?

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The area of the square is 15129 square units.

Explanation

The area of a square = side².

 

The side length is given as √15129.

 

Area of the square = side² = √15129 × √15129 = 123 × 123 = 15129.

 

Therefore, the area of the square box is 15129 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 15129 square feet is built. If each of the sides is √15129, what will be the square feet of half of the building?

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7564.5 square feet

Explanation

To find half of the building's square feet, divide the given area by 2.

 

Dividing 15129 by 2 = 7564.5

 

So half of the building measures 7564.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √15129 × 5.

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615

Explanation

First, find the square root of 15129, which is 123.

 

Then multiply 123 by 5. So, 123 × 5 = 615.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (15129 + 0)?

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The square root is 123.

Explanation

To find the square root, calculate 15129 + 0 = 15129, and then √15129 = 123.

 

Therefore, the square root of (15129 + 0) is ±123.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √15129 units and the width ‘w’ is 38 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The perimeter of the rectangle is 322 units.

Explanation

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

 

Perimeter = 2 × (√15129 + 38) = 2 × (123 + 38) = 2 × 161 = 322 units.

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FAQ on Square Root of 15129

1.What is √15129 in its simplest form?

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2.What are the factors of 15129?

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3.Calculate the square of 15129.

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4.Is 15129 a prime number?

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5.What is the significance of 15129 being a perfect square?

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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 15129?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 15129?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 15129

  • Square root: The square root is the inverse of a square. For example, 123² = 15129, and the inverse of the square is the square root, so √15129 = 123. 

 

  • Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers. 

 

  • Perfect square: A perfect square is a number that is the square of an integer. For example, 15129 is a perfect square because its square root is 123. 

 

  • Prime factorization: Prime factorization is the process of decomposing a number into its prime factors. For example, the prime factorization of 15129 is 3² × 41². 

 

  • Long division method: A method used to find the square root of a number by performing division in a structured manner.
Professor Greenline from BrightChamps

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 15129 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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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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