Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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
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.
Calculate √(25/4) × 5.
12.5
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.
What will be the square root of (25/4 + 0)?
The square root is 2.5
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.
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.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (2.5 + 4)
= 2 × 6.5
= 13 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.