116 LearnersLast updated on May 26th, 2025
Square Root of 1/25
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.
What is 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.
Finding the Square Root of 1/25
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1/25 by Prime Factorization Method
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.
Square Root of 1/25 by Long Division Method
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.
Square Root of 1/25 by Approximation Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 1/25
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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the principal (positive) square root, as it is the required one.
For example, √(1/25) = 1/5, there is also -1/5 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before proceeding.
For example, √(4/25) = √4/√25 is correct, but √(4/25) = 2/√25 is not.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example, √(1/27) ≈ 0.192, not 0.18.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example, √(1/27) and ∛(1/27) are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end. This may happen during subtraction or elsewhere.
Square Root of 1/25 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √(1/25) x 5.
1
Explanation
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.
Problem 4
What will be the square root of (1/25 + 24/25)?
The square root is 1.
Explanation
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.
Problem 5
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.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (1/5 + 10) = 2 × (0.2 + 10) = 2 × 10.2 = 20.4 units.
FAQ on Square Root of 1/25
1.What is √(1/25) in its simplest form?
2.Mention the factors of 25.
3.Calculate the square of 1/5.
4.Is 1/25 a perfect square?
5.1/25 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 1/25?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1/25?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 1/25
- Square root: A square root is the inverse of a square. Example: 5² = 25, and the inverse of the square is the square root, that is, √25 = 5.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 25 is a perfect square because it is 5².
- Rational number: A rational number is a number that can be expressed in the form of p/q, where q ≠ 0 and p and q are integers.
- Decimal: A decimal is a number that has a whole number and a fraction in a single number, such as 0.2, 1.5, and 3.75.
- Principal square root: The principal square root is the positive square root of a number. For example, the principal square root of 25 is 5.
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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.
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