123 LearnersLast updated on May 26th, 2025
Square Root of 25/4
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 25/4.
What is the Square Root of 25/4?
The square root is the inverse of the square of the number. 25/4 is a perfect square. The square root of 25/4 can be expressed in both radical and exponential form. In the radical form, it is expressed as √(25/4), whereas (25/4)^(1/2) in the exponential form. √(25/4) = 5/2 = 2.5, 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 25/4
The prime factorization method and direct calculation can be used for perfect square numbers. Since 25/4 is a perfect square, we can directly calculate its square root. Let us now learn the following method:
- Direct Calculation Method
Square Root of 25/4 by Direct Calculation Method
Since 25/4 is a fraction, we can find its square root by finding the square root of the numerator and the denominator separately.
Step 1: Find the square root of the numerator, which is 25. The square root of 25 is 5.
Step 2: Find the square root of the denominator, which is 4. The square root of 4 is 2.
Step 3: Combine the square roots to form a fraction.
Therefore, the square root of 25/4 is 5/2, which is equal to 2.5.
Common Mistakes and How to Avoid Them in the Square Root of 25/4
Students do make mistakes while finding the square root, such as forgetting about the negative square root or not simplifying the fraction properly. Let us look at a few of these mistakes in detail.
Common Mistakes and How to Avoid Them in the Square Root of 25/4
Students do make mistakes while finding the square root, such as forgetting about the negative square root or not simplifying fractions properly. Let us look at a few of these 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, we usually consider only the principal (positive) square root unless specified otherwise.
For example, the square root of 25/4 is ±2.5, but we focus on 2.5.
Mistake 2
Incorrect simplification of fractions
Sometimes students fail to simplify fractions correctly before finding the square root. Ensure that fractions are in their simplest form.
For instance, the square root of 100/16 should first simplify the fraction to 25/4 before calculating the square root.
Mistake 3
Confusing the square root of a fraction with individual roots
Students may confuse the process by not calculating the square roots of the numerator and denominator separately.
For example, √(25/4) should be calculated as √25/√4 = 5/2, not as √(25/4) = √6.25.
Mistake 4
Not considering both roots in fraction form
Students sometimes forget to consider both the numerator and denominator in the fraction. Always find the square root of both the numerator and the denominator separately to get an accurate result.
Mistake 5
Confusing square roots with cube roots
Ensure that there is a clear distinction between square roots and cube roots.
For example, √(25/4) is not the same as ∛(25/4). They have different meanings and results.
Square Root of 25/4 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(25/4)?
The area of the square is 6.25 square units.
Explanation
The area of the square = side².
The side length is given as √(25/4) = 5/2 = 2.5.
Area of the square = side²
= 2.5 × 2.5
= 6.25.
Therefore, the area of the square box is 6.25 square units.
Problem 2
A square-shaped garden measuring 25/4 square meters is built; if each of the sides is √(25/4), what will be the square meters of half of the garden?
3.125 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 25/4 by 2 = (25/4) / 2 = 25/8 = 3.125.
So half of the garden measures 3.125 square meters.
Problem 3
Calculate √(25/4) × 5.
12.5
Explanation
The first step is to find the square root of 25/4, which is 2.5. The second step is to multiply 2.5 by 5. So, 2.5 × 5 = 12.5.
Problem 4
What will be the square root of (25/4 + 0)?
The square root is 2.5
Explanation
To find the square root, we need to determine the sum of (25/4 + 0). 25/4 + 0 = 25/4, and then √(25/4) = 2.5.
Therefore, the square root of (25/4 + 0) is ±2.5.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(25/4) units and the width ‘w’ is 4 units.
We find the perimeter of the rectangle as 13 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (2.5 + 4)
= 2 × 6.5
= 13 units.
FAQ on Square Root of 25/4
1.What is √(25/4) in its simplest form?
2.Mention the factors of 25/4.
3.Calculate the square of 25/4.
4.Is 25/4 a rational number?
5.Is 25/4 a perfect square?
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 25/4?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 25/4?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 25/4
- 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, that is √16 = 4.
- Rational number: A rational number is a number that can be written in the form of p/q, where p and q are integers and q is not equal to zero.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 25 and 4 are perfect squares because they are squares of 5 and 2, respectively.
- Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It is expressed as the quotient of two numbers, the numerator over the denominator.
- Principal square root: A number has both positive and negative square roots; however, it is usually the positive square root that is used in real-world applications. This is known as the principal square root.
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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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