146 LearnersLast updated on May 26th, 2025
Square Root of 12544
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 12544
What is the Square Root of 12544?
The square root is the inverse of the square of a number. 12544 is a perfect square. The square root of 12544 is expressed in both radical and exponential form. In the radical form, it is expressed as √12544, whereas (12544)(1/2) in the exponential form. √12544 = 112, 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.
Finding the Square Root of 12544
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 12544 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 12544 is broken down into its prime factors.
Step 1: Finding the prime factors of 12544 Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7: 2^6 × 7^2
Step 2: Now we found out the prime factors of 12544. The second step is to make pairs of those prime factors.
Since 12544 is a perfect square, we can group the digits into pairs: (26 × 72) = (23 × 7)2 = (8 × 7)2 = 562. Therefore, the square root of 12544 using prime factorization is 56.
Square Root of 12544 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin, we need to group the numbers from right to left. In the case of 12544, we need to group it as 44 and 125.
Step 2: Now, we need to find n whose square is closest to 125. We can say n is '11' because 11 × 11 = 121, which is less than 125. Now the quotient is 11, and after subtracting 121 from 125, the remainder is 4.
Step 3: Now, let us bring down 44 to make the new dividend 444.
Step 4: The new divisor will be the sum of the old divisor and the quotient doubled, which is 22.
Step 5: We now need to find a number that, when multiplied by (220 + n), is less than or equal to 444. This number is 2, as 222 × 2 = 444.
Step 6: Subtracting 444 from 444, the remainder is 0, and the quotient is 112. Therefore, the square root of 12544 is 112.
Square Root of 12544 by Approximation Method
The approximation method is another method for finding square roots, and it can be used for both perfect and non-perfect squares. However, for perfect squares like 12544, the exact square root is preferred.
Step 1: Now we have to find the closest perfect square of √12544. 12544 is a perfect square, so the square root is exactly 112.
Common Mistakes and How to Avoid Them in the Square Root of 12544
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division methods. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one. For example: √64 = 8, but there is also -8, which should not be forgotten.
Square Root of 12544 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √144?
The area of the square is 144 square units.
Explanation
The area of the square = side2. The side length is given as √144.
Area of the square = side2 = √144 × √144 = 12 × 12 = 144
Therefore, the area of the square box is 144 square units.
Problem 2
A square-shaped building measuring 12544 square feet is built; if each of the sides is √12544, what will be the square feet of half of the building?
6272 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 12544 by 2 = 6272
So half of the building measures 6272 square feet.
Problem 3
Calculate √12544 × 5.
560
Explanation
The first step is to find the square root of 12544, which is 112.
The second step is to multiply 112 by 5.
So 112 × 5 = 560
Problem 4
What will be the square root of (121 + 4)?
The square root is 11.
Explanation
To find the square root, we need to find the sum of (121 + 4). 121 + 4 = 125, and then √125 is approximately 11.18, but for perfect squares, √121 = 11.
Therefore, the square root of (121 + 4) is approximately 11.18 for non-perfect squares.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √144 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 100 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√144 + 38) = 2 × (12 + 38) = 2 × 50 = 100 units.
FAQ on Square Root of 12544
1.What is √12544 in its simplest form?
2.Mention the factors of 12544.
3.Calculate the square of 12544.
4.Is 12544 a prime number?
5.12544 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 12544?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 12544?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 12544
- 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.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 36 is a perfect square because it is 62.
- Rational number: A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to zero.
- Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors.
- Long division method: The long division method is a technique used to find the square root of a number by dividing and averaging.
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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.
