102 LearnersLast updated on May 26th, 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.
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.
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 √(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 √2 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 √(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 √2 units and the width 'w' is √(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 √(1/6) in its simplest form?
2.What is the decimal value of √(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).
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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.
