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341 LearnersLast updated on August 5, 2025
Square Root of 1/6
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 1/6.
What is the Square Root of 1/6?
The square root is the inverse of the square of a number. 1/6 is not a perfect square. The square root of 1/6 is expressed in both radical and exponential form. In radical form, it is expressed as √(1/6), whereas (1/6)^(1/2) in exponential form. √(1/6) = 0.40825, 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 1/6
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 1/6 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Since 1/6 is a fraction, we need to consider the prime factorization of 6.
Step 1: Finding the prime factors of 6 Breaking it down, we get 2 x 3.
Step 2: Now we found out the prime factors of 6. Since 1/6 is not a perfect square, calculating √(1/6) using prime factorization requires rewriting it as a fraction of two square roots: √1/√6.
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Square Root of 1/6 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, let's find the square root of 1 and 6 separately.
Step 2: √1 is 1.
Step 3: Using the long division method or a calculator, find the square root of 6, which is approximately 2.44949.
Step 4: Now, divide 1 by 2.44949 to get the square root of 1/6.
Step 5: The result is approximately 0.40825.
Square Root of 1/6 by Approximation Method
The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1/6 using the approximation method.
Step 1: We already know that √1 is 1.
Step 2: We find that the square root of 6 is approximately 2.44949.
Step 3: Dividing 1 by 2.44949 gives us approximately 0.40825, which is the square root of 1/6.
Common Mistakes and How to Avoid Them in the Square Root of 1/6
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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 positive square root, as it is the required one.
For example: √1/6 = ±0.40825, but we often use just the positive value.
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 and then move on to the second step.
For example: √(1/6) is not the same as √1/√6.
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: √6 ≈ 2.44949, not 2.
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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1/6 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ(1/6)?
The area of the square is approximately 0.1667 square units.
Explanation
The area of the square = side².
The side length is given as √(1/6).
Area of the square = side²
= (√(1/6))²
= 1/6
≈ 0.1667.
Therefore, the area of the square box is approximately 0.1667 square units.
Problem 2
A rectangle measures 1/6 square feet in area. If one side is โ2 feet, what is the length of the other side?
The length of the other side is approximately 0.2041 feet.
Explanation
Using the area formula for a rectangle, Area = length × width.
Given Area = 1/6 and one side (width) = √2,
Length = Area/Width
= (1/6)/√2
= √(1/6)
= 0.40825.
Dividing gives approximately 0.2041 feet for the other side.
Problem 3
Calculate โ(1/6) x 10.
Approximately 4.0825
Explanation
The first step is to find the square root of 1/6, which is approximately 0.40825.
The second step is to multiply 0.40825 with 10.
So 0.40825 × 10 = 4.0825.
Problem 4
What will be the square root of (1/6 + 1/3)?
The square root is approximately 0.5774.
Explanation
To find the square root, we need to find the sum of (1/6 + 1/3).
1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 0.5, and then the square root of 0.5 ≈ 0.7071.
Therefore, the square root of (1/6 + 1/3) is approximately ±0.7071.
Problem 5
Find the perimeter of a rectangle if its length 'l' is โ2 units and the width 'w' is โ(1/6) units.
The perimeter of the rectangle is approximately 5.6325 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2 + √(1/6))
≈ 2 × (1.4142 + 0.40825)
= 2 × 1.82245
≈ 5.6325 units.
FAQ on Square Root of 1/6
1.What is โ(1/6) in its simplest form?
2.What is the decimal value of โ(1/6)?
3.Calculate the square of 1/6.
4.Is 1/6 a rational number?
5.What numbers are used to express 1/6 in terms of its prime factors?
Important Glossaries for the Square Root of 1/6
- Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It is represented as a ratio of two integers, for example, 1/6.
- Decimal approximation: This is an approximate representation of a number in decimal form. For example, the square root of 1/6 is approximately 0.40825.
- Perimeter: The perimeter is the distance around a two-dimensional shape. For a rectangle, it is calculated as 2 × (length + width).
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.
