Square Root of 1/6
2026-02-28 06:17 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1/6

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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 1/6.

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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/6)?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(1/6) x 10.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (1/6 + 1/3)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √2 units and the width 'w' is √(1/6) units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 1/6

1.What is √(1/6) in its simplest form?

√(1/6) can be written as √1/√6. Since 1 is a perfect square, √1 = 1, so the simplest form is 1/√6.

2.What is the decimal value of √(1/6)?

The decimal value of √(1/6) is approximately 0.40825.

3.Calculate the square of 1/6.

We get the square of 1/6 by multiplying the number by itself, that is (1/6) × (1/6) = 1/36.

4.Is 1/6 a rational number?

Yes, 1/6 is a rational number because it can be expressed as p/q, where p and q are integers and q ≠ 0.

5.What numbers are used to express 1/6 in terms of its prime factors?

The number 6 can be expressed in terms of its prime factors as 2 × 3. Therefore, 1/6 in terms of prime factors involves 1/(2 × 3).

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.