122 LearnersLast updated on May 26th, 2025
Square Root of 13154
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 13154.
What is the Square Root of 13154?
The square root is the inverse of the square of a number. 13154 is not a perfect square. The square root of 13154 is expressed in both radical and exponential forms. In the radical form, it is expressed as √13154, whereas (13154)(1/2) in the exponential form. √13154 ≈ 114.672, 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.
Finding the Square Root of 13154
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where the long division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 13154 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 13154 is broken down into its prime factors.
Step 1: Finding the prime factors of 13154 Breaking it down, we get 2 x 6577: 21 x 6577
Step 2: Now we found out the prime factors of 13154. Since 13154 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 13154 using prime factorization is impossible.
Square Root of 13154 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. 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 13154, we need to group it as 54 and 131.
Step 2: Now we need to find n whose square is less than or equal to 131. We can say n is ‘11’ because 11 x 11 = 121, which is less than 131. Now the quotient is 11, and after subtracting 121 from 131, the remainder is 10.
Step 3: Now let us bring down 54, which is the new dividend. Add 11 with itself to get 22, which will be our new divisor.
Step 4: The next step is finding n such that 22n x n is less than or equal to 1054.
Step 5: Let us consider n as 4, so 224 x 4 = 896.
Step 6: Subtract 896 from 1054, and the difference is 158, and the new quotient becomes 114.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 15800.
Step 8: Now we need to find the new divisor. Add 4 to 224 to get 228, and find n such that 228n x n is less than or equal to 15800.
Step 9: Continue performing these steps until you get two digits after the decimal point. So the square root of √13154 is approximately 114.672.
Square Root of 13154 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 13154 using the approximation method.
Step 1: Now we have to find the closest perfect square of √13154. The smallest perfect square less than 13154 is 12996 (1142) and the largest perfect square greater than 13154 is 13225 (1152). √13154 falls somewhere between 114 and 115.
Step 2: Now we need to apply linear interpolation between these two squares: Using the formula: (given number - smaller perfect square) / (larger perfect square - smaller perfect square)
(13154 - 12996) / (13225 - 12996) ≈ 0.672
Adding this decimal to the smaller integer root: 114 + 0.672 = 114.672
Thus, the square root of 13154 is approximately 114.672.
Common Mistakes and How to Avoid Them in the Square Root of 13154
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at some common mistakes made by students in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically focus on the positive square root, as it is more commonly used. For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Square Root of 13154 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √13154?
The area of the square is approximately 13154 square units.
Explanation
The area of the square = side2.
The side length is given as √13154.
Area of the square = side2 = √13154 x √13154 = 13154.
Therefore, the area of the square box is approximately 13154 square units.
Problem 2
A square-shaped building measuring 13154 square feet is built; if each of the sides is √13154, what will be the square feet of half of the building?
6577 square feet
Explanation
We divide the given area by 2 as the building is square-shaped.
Dividing 13154 by 2 = 6577
So half of the building measures 6577 square feet.
Problem 3
Calculate √13154 x 3.
344.016
Explanation
The first step is to find the square root of 13154, which is approximately 114.672.
The second step is to multiply 114.672 by 3.
So 114.672 x 3 ≈ 344.016.
Problem 4
What will be the square root of (13154 + 81)?
The square root is 116.
Explanation
To find the square root, we need to find the sum of (13154 + 81). 13154 + 81 = 13225, and then √13225 = 115.
Therefore, the square root of (13154 + 81) is ±115.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √13154 units and the width ‘w’ is 100 units.
The perimeter of the rectangle is approximately 429.344 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√13154 + 100) = 2 × (114.672 + 100) = 2 × 214.672 = 429.344 units.
FAQ on Square Root of 13154
1.What is √13154 in its simplest form?
2.Mention the factors of 13154.
3.Calculate the square of 13154.
4.Is 13154 a prime number?
5.13154 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 13154?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 13154?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 13154
- Square root: A square root is the inverse of a square. Example: 42 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is typically used more often due to its real-world applications. This is known as the principal square root.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Long division method: A method to find the square root of a non-perfect square by breaking it down into smaller steps, involving division and subtraction.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
