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Last updated on May 26th, 2025

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Square Root of 1/5

Professor Greenline Explaining Math Concepts

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.

Square Root of 1/5 for Global Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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

Professor Greenline from BrightChamps

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

Max Pointing Out Common Math Mistakes

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:

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. However, we typically consider only the positive square root for practical applications.

For example: √(1/5) ≈ 0.447, but there is also -0.447.

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Square Root of 1/5 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √(1/5) x 5.

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 1/5

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

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2.Mention the factors of 5.

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3.Calculate the square of 1/5.

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4.Is 1/5 a prime number?

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5.What is 1/5 as a decimal?

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Professor Greenline from BrightChamps

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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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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