122 LearnersLast updated on May 26th, 2025
Square Root of 25.25
If a number is multiplied by itself, 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 and finance. Here, we will discuss the square root of 25.25.
What is the Square Root of 25.25?
The square root is the inverse of the square of the number. 25.25 is not a perfect square. The square root of 25.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √25.25, whereas (25.25)^(1/2) in the exponential form. √25.25 = 5.0249378106, 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 25.25
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 25.25 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: Start by grouping the digits from right to left in pairs. For 25.25, consider 25 and 25 as separate groups.
Step 2: Find a number whose square is less than or equal to 25. The number is 5, since 5 × 5 = 25. The quotient is 5, and the remainder is 0.
Step 3: Bring down the next pair, which is 25, and place it next to the remainder, making it 025. Add the previous divisor, 5, to itself to get 10.
Step 4: Find a number (n) such that 10n × n ≤ 25. The number is 2, as 102 × 2 = 204, which is less than 250.
Step 5: Subtract 204 from 250, leaving a remainder of 46.
Step 6: Bring down another pair of zeros to make the number 4600.
Step 7: Continue the process until you reach the desired precision.
The quotient, up to two decimal places, is 5.02.
Square Root of 25.25 by Approximation Method
The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 25.25 using the approximation method.
Step 1: Identify the closest perfect squares to 25.25. The closest perfect squares are 25 (5²) and 36 (6²).
Step 2: Apply the formula:
(Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square).
Step 3: Using the formula, (25.25 - 25) ÷ (36 - 25) = 0.25 ÷ 11 = 0.0227.
Step 4: Add this to the square root of the smaller perfect square: 5 + 0.0227 = 5.0227.
This approximation gives the square root of 25.25 as approximately 5.024.
Common Mistakes and How to Avoid Them in the Square Root of 25.25
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, in most contexts, we consider only the principal (positive) square root.
For example, √25.25 = ±5.0249378106, but typically we use the positive value.
Square Root of 25.25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √25.25?
The area of the square is 25.25 square units.
Explanation
The area of a square is given by side².
The side length is √25.25, so the area is (√25.25)² = 25.25 square units.
Problem 2
A square-shaped building measuring 25.25 square feet is built; if each side is √25.25, what will be the square feet of half of the building?
12.625 square feet
Explanation
Divide the given area by 2 as the building is square-shaped.
Dividing 25.25 by 2 gives 12.625 square feet.
Problem 3
Calculate √25.25 × 5.
25.124689053
Explanation
First, find the square root of 25.25, which is approximately 5.0249378106.
Then multiply by 5: 5.0249378106 × 5 = 25.124689053.
Problem 4
What will be the square root of (20 + 5.25)?
The square root is 5.0249378106
Explanation
To find the square root, sum (20 + 5.25) = 25.25, and then find √25.25 ≈ 5.0249378106.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √25.25 units and the width ‘w’ is 8 units.
The perimeter of the rectangle is 26.0498756212 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√25.25 + 8) = 2 × (5.0249378106 + 8) = 2 × 13.0249378106 = 26.0498756212 units.
FAQ on Square Root of 25.25
1.What is √25.25 in its simplest form?
2.Mention the factors of 25.25.
3.Calculate the square of 25.25.
4.Is 25.25 a prime number?
5.25.25 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 25.25?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 25.25?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 25.25
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √25.25 ≈ 5.0249.
- Irrational number: An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion.
- Principal square root: The principal square root is the positive square root of a number. For example, the principal square root of 25.25 is 5.0249378106.
- Decimal: A decimal is a fraction written in a special form. For example, 0.5 is a decimal and is equal to 1/2.
- Approximation: An approximation is a value or quantity that is nearly but not exactly correct. It is used to estimate values when precise figures are not necessary.
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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.
