Square Root of 1/5
2026-02-28 06:15 Diff
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Last updated on August 5, 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1/5.

What is the Square Root of 1/5?

The square root is the inverse of the square of the number. 1/5 is not a perfect square. The square root of 1/5 is expressed in both radical and exponential form. In radical form, it is expressed as √(1/5), whereas (1/5)^(1/2) in exponential form. √(1/5) = √1/√5 = 1/√5 = √5/5, 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 1/5

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods: 

  • Prime factorization method 
  • Long division method
  • Approximation method

Square Root of 1/5 by Prime Factorization Method

Since 1/5 is a fraction, prime factorization of the numerator and denominator separately doesn't yield a straightforward result like for integers.

Therefore, calculating 1/5 using prime factorization is not applicable. Instead, it is more helpful to consider the square root of the numerator and the square root of the denominator separately, which gives √1/√5 = 1/√5 = √5/5.

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Square Root of 1/5 by Long Division Method

The long division method is particularly used for non-perfect square numbers, including fractions. In this method, we can convert the fraction into a decimal and then apply the long division method. Here’s how to find the square root using the long division method, step by step:

Step 1: Convert 1/5 into a decimal, which is 0.2.

Step 2: Group the digits of 0.2, considering pairs of two digits from right to left. Here, it becomes 0.20.

Step 3: Find a number whose square is less than or equal to 0.20. The number is 0.4 because 0.4 * 0.4 = 0.16, which is less than 0.20.

Step 4: Subtract 0.16 from 0.20 to get 0.04.

Step 5: Bring down two zeros, making the new dividend 400.

Step 6: Double the quotient (0.4) to get 0.8 and find a digit such that 0.8x * x is close to 400. The digit is 5 because 0.85 * 5 ≈ 0.425.

Step 7: The quotient becomes 0.45, which is approximately the square root of 0.2.

The square root of 1/5 ≈ 0.447

Square Root of 1/5 by Approximation Method

The approximation method is another way to find square roots, especially for non-perfect squares. Here is how to find the square root of 1/5 using the approximation method:

Step 1: Convert 1/5 into a decimal, which is 0.2.

Step 2: Notice that 0.2 lies between the perfect squares 0.16 (0.4^2) and 0.25 (0.5^2).

Step 3: We can estimate that the square root of 0.2 is between 0.4 and 0.5.

Step 4: Use interpolation: (0.2 - 0.16) / (0.25 - 0.16) = 0.04 / 0.09 ≈ 0.44. By interpolation, 0.4 + 0.44(0.1) = 0.44.

So, the square root of 1/5 ≈ 0.447

Common Mistakes and How to Avoid Them in the Square Root of 1/5

Students make mistakes while finding square roots, such as misunderstanding the negative square root or misapplying methods. Here are a few common mistakes:

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/5)?

Okay, lets begin

The area of the square is 0.04 square units.

Explanation

The area of the square = side^2.

The side length is given as √(1/5).

Area of the square = (√(1/5))^2

= 1/5

= 0.2.

Therefore, the area of the square box is 0.04 square units.

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Problem 2

A square-shaped building measuring 1/5 square units is built; if each of the sides is √(1/5), what will be the square units of half of the building?

Okay, lets begin

0.1 square units

Explanation

We can divide the given area by 2 because the building is square-shaped.

Dividing 1/5 by 2 = 1/10 = 0.1.

So half of the building measures 0.1 square units.

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Problem 3

Calculate √(1/5) x 5.

Okay, lets begin

2.236

Explanation

The first step is to find the square root of 1/5, which is approximately 0.447.

The second step is to multiply 0.447 by 5.

So, 0.447 x 5 ≈ 2.236.

Well explained 👍

Problem 4

What will be the square root of (1/5 + 4/5)?

Okay, lets begin

The square root is 1.

Explanation

To find the square root, first find the sum of (1/5 + 4/5).

1/5 + 4/5 = 1, and then √1 = 1.

Therefore, the square root of (1/5 + 4/5) is ±1.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(1/5) units and the width ‘w’ is 3 units.

Okay, lets begin

The perimeter of the rectangle is approximately 6.894 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√(1/5) + 3)

= 2 × (0.447 + 3)

≈ 2 × 3.447

= 6.894 units.

Well explained 👍

FAQ on Square Root of 1/5

1.What is √(1/5) in its simplest form?

The simplest form of √(1/5) is √5/5, which is approximately 0.447.

2.Mention the factors of 5.

3.Calculate the square of 1/5.

The square of 1/5 is (1/5) × (1/5) = 1/25 = 0.04.

4.Is 1/5 a prime number?

1/5 is not a prime number because it is a fraction, not an integer.

5.What is 1/5 as a decimal?

Important Glossaries for the Square Root of 1/5

  • Square root: A square root is the inverse operation of squaring a number. For example, if x^2 = 9, then √9 = 3.
     
  • Irrational number: An irrational number is a number that cannot be written as a simple fraction; √5 is an example.
     
  • Fraction: A fraction represents a part of a whole. It consists of a numerator and a denominator. Example: 1/5.
     
  • Decimal: A decimal is a fraction expressed in a special form. For example, 0.2 is the decimal form of 1/5.
     
  • Principal square root: The principal square root is the non-negative root of a number. For example, the principal square root of 9 is 3.

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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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