127 LearnersLast updated on May 26th, 2025
Square Root of 12.5
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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 12.5.
What is the Square Root of 12.5?
The square root is the inverse of the square of the number. 12.5 is not a perfect square. The square root of 12.5 is expressed in both radical and exponential form. In the radical form, it is expressed as √12.5, whereas (12.5)^(1/2) in the exponential form. √12.5 ≈ 3.5355339, 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 12.5
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 12.5 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. 12.5 is not an integer, so it cannot be directly factored using prime factorization. Thus, the prime factorization method is not applicable for non-integers like 12.5.
Square Root of 12.5 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, consider the number 12.5. Move the decimal two places to the right, making it 1250.
Step 2: Group the digits into pairs starting from the decimal point. Consider 12 and 50.
Step 3: Find a number whose square is less than or equal to 12. The number is 3, since 3 × 3 = 9.
Step 4: Subtract 9 from 12, giving 3. Bring down the next pair, 50, to make it 350.
Step 5: Double the divisor (3) to get 6, and determine the next digit of the quotient as 5, because 65 × 5 = 325.
Step 6: Subtract 325 from 350, giving a remainder of 25.
Step 7: Bring down two zeros to make it 2500.
Step 8: The new divisor is 705. Determine the next digit of the quotient. Continue until the desired precision is reached.
So, the square root of 12.5 ≈ 3.5355.
Square Root of 12.5 by Approximation Method
Approximation method is another method for finding square roots. It is an easy way to find the square root of a given number. Let us learn how to find the square root of 12.5 using the approximation method.
Step 1: Find the closest perfect squares to 12.5. The smallest perfect square is 9, and the largest perfect square is 16. √12.5 falls between 3 and 4.
Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (12.5 - 9) / (16 - 9) = 3.5 / 7 = 0.5
Step 3: Add this value to the smaller number, which is 3.
Therefore, 3 + 0.5 = 3.5, which is an approximation of the square root of 12.5.
Common Mistakes and How to Avoid Them in the Square Root of 12.5
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Let us look at a few of these mistakes 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 will consider only the positive square root, as it is the required one.
For example, √12.5 ≈ 3.5355, but there is also -3.5355 which should not be forgotten.
Square Root of 12.5 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √12.5?
The area of the square is approximately 12.5 square units.
Explanation
The area of the square = side².
The side length is given as √12.5.
Area of the square = side² = √12.5 × √12.5 = 12.5.
Therefore, the area of the square box is approximately 12.5 square units.
Problem 2
A square-shaped building measuring 25 square feet is built; if each of the sides is √12.5, what will be the square feet of half of the building?
Approximately 12.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 25 by 2, we get approximately 12.5.
So, half of the building measures approximately 12.5 square feet.
Problem 3
Calculate √12.5 × 5.
Approximately 17.677
Explanation
The first step is to find the square root of 12.5, which is approximately 3.5355.
The second step is to multiply 3.5355 by 5.
So, 3.5355 × 5 ≈ 17.677.
Problem 4
What will be the square root of (12.5 + 2.5)?
The square root is approximately 4.
Explanation
To find the square root, we need to find the sum of (12.5 + 2.5). 12.5 + 2.5 = 15, and then √15 ≈ 3.872.
Therefore, the square root of (12.5 + 2.5) is approximately 3.872.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √12.5 units and the width ‘w’ is 5 units.
The perimeter of the rectangle is approximately 17.071 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√12.5 + 5) = 2 × (3.5355 + 5) ≈ 2 × 8.5355 ≈ 17.071 units.
FAQ on Square Root of 12.5
1.What is √12.5 in its simplest form?
2.What are the factors of 12.5?
3.Calculate the square of 12.5.
4.Is 12.5 a prime number?
5.What is 12.5 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 12.5?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 12.5?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 12.5
- Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, which 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, it is always the positive square root that has more prominence due to its uses in the real world. This is why it is also 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 used to find the square root of non-perfect square numbers, involving a series of division steps to approximate the value.
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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
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