248 LearnersLast updated on May 26th, 2025
Square Root of 15129
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.
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.
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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: -
- Prime factorization method
- Long division method
- Approximation method
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.
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.
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.
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
Forgetting about the Negative Square Root
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.
Mistake 2
Not Adding Square Root Symbol in Proper Places
Incorrect placement of the square root symbol is a common mistake. It is crucial to simplify numbers inside the square root before further calculations. For example, √(16 + 9) = √25 = 5, not √16 + √9 = 4 + 3.
Mistake 3
Not Finding the Correct Value of a Non-Perfect Square
Students should be taught to simplify numbers inside the square root to find accurate approximations. For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the Square Root Symbol with the Cube Root
Students should understand the difference between cube roots and square roots to avoid confusion. For example: √64 and ∛64 are different—√64 = 8 and ∛64 = 4.
Mistake 5
Making Mistakes in Long Division
The long division method involves several steps, and students may accidentally skip a step, leading to incorrect answers. This can occur during subtraction or elsewhere.
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Square Root of 15129 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √15129?
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.
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?
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.
Problem 3
Calculate √15129 × 5.
615
Explanation
First, find the square root of 15129, which is 123.
Then multiply 123 by 5. So, 123 × 5 = 615.
Problem 4
What will be the square root of (15129 + 0)?
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.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √15129 units and the width ‘w’ is 38 units.
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?
2.What are the factors of 15129?
3.Calculate the square of 15129.
4.Is 15129 a prime number?
5.What is the significance of 15129 being a perfect square?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 15129?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 15129?
9.Does learning Algebra support future career opportunities for students in United States?
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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.
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Jaskaran Singh Saluja
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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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