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 1/25.
The square root is the inverse of the square of the number. 1/25 is a perfect square. The square root of 1/25 is expressed in both radical and exponential form. In radical form, it is expressed as √(1/25), whereas (1/25)^(1/2) in exponential form. √(1/25) = 1/5, 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 is used for perfect square numbers. Since 1/25 is a perfect square, we can use the prime factorization method. Alternatively, the long division method and approximation method are also suitable for verification. Let us now learn the following methods:
The product of prime factors is the prime factorization of a number. Now let us look at how 25 is broken down into its prime factors:
Step 1: Finding the prime factors of 25 Breaking it down, we get 5 x 5: 5²
Step 2: Since 1 is already a perfect square (1²), the prime factorization of 1/25 is 1/(5²).
Step 3: Taking the square root of 1/25 gives us 1/5.
The long division method is another method that can be used for perfect square numbers. Here is how you find the square root of 1/25 using long division:
Step 1: Express 1/25 as a decimal, which is 0.04.
Step 2: Group the digits of 0.04 as 00 and 04.
Step 3: Find a number whose square is closest to 0.04. Here, 0.2 x 0.2 = 0.04.
Step 4: Therefore, the square root of 0.04 is 0.2, which equals 1/5.
The approximation method is another method for finding square roots. It's an easy method to understand the square root of a given number. Let's learn how to find the square root of 1/25 using the approximation method:
Step 1: Approximate 1/25 to the nearest perfect square. The closest perfect square to 0.04 is 0.04 itself.
Step 2: The square root of 0.04 is 0.2.
Step 3: Therefore, the square root of 1/25 is 1/5.
Students can make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √(1/25)?
The area of the square is 1/25 square units.
The area of the square = side².
The side length is given as √(1/25), which is 1/5.
Area of the square = (1/5)² = 1/25.
Therefore, the area of the square box is 1/25 square units.
A square-shaped building measuring 1/25 square meters is built; if each of the sides is √(1/25), what will be the square meters of half of the building?
1/50 square meters
We can divide the given area by 2 as the building is square-shaped.
Dividing 1/25 by 2 = 1/50.
So, half of the building measures 1/50 square meters.
Calculate √(1/25) x 5.
1
The first step is to find the square root of 1/25, which is 1/5.
The second step is to multiply 1/5 by 5.
So, (1/5) x 5 = 1.
What will be the square root of (1/25 + 24/25)?
The square root is 1.
To find the square root, we need to find the sum of (1/25 + 24/25). 1/25 + 24/25 = 25/25 = 1, and then √1 = ±1. Therefore, the square root of (1/25 + 24/25) is ±1.
Find the perimeter of the rectangle if its length ‘l’ is √(1/25) units and the width ‘w’ is 10 units.
The perimeter of the rectangle is 20.4 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (1/5 + 10) = 2 × (0.2 + 10) = 2 × 10.2 = 20.4 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.
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