130 LearnersLast updated on May 26th, 2025
Square Root of 1/5
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.
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:
Mistake 1
Forgetting about the negative square root
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.
Mistake 2
Not adding the square root symbol in proper places
A common mistake is not using the square root symbol correctly. To avoid this, it's important to first simplify the expression inside the square root.
For example: √(1 + 4) = √5, not √1 + √4.
Mistake 3
Not finding the correct value of a non-perfect square
Students should simplify the numbers inside the square root to find the approximate value.
For example: √(1/5) ≈ 0.447, not 0.45 or 0.4.
Mistake 4
Confusing the square root symbol with the cube root
Students should understand the difference between cube roots and square roots to avoid confusion.
For example, √(1/5) is different from ∛(1/5).
Mistake 5
Making mistakes in converting fractions to decimals
While converting fractions into decimals, students might make errors.
For example, 1/5 should be converted to 0.2 correctly before proceeding with further calculations.
Square Root of 1/5 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(1/5)?
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.
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?
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.
Problem 3
Calculate √(1/5) x 5.
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.
Problem 4
What will be the square root of (1/5 + 4/5)?
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.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(1/5) units and the width ‘w’ is 3 units.
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.
FAQ on Square Root of 1/5
1.What is √(1/5) in its simplest form?
2.Mention the factors of 5.
3.Calculate the square of 1/5.
4.Is 1/5 a prime number?
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
