Square Root of 1/81
2026-02-28 06:11 Diff
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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 1/81.

What is the Square Root of 1/81?

The square root is the inverse of the square of the number. 1/81 is a perfect square. The square root of 1/81 is expressed in both radical and exponential form. In the radical form, it is expressed as, √(1/81), whereas (1/81)^(1/2) in the exponential form. √(1/81) = 1/9, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 1/81

The prime factorization method is useful for finding the square roots of perfect squares. For non-perfect squares, methods such as long division and approximation are used. Since 1/81 is a perfect square, let's use the prime factorization method:

  • Prime factorization method

Square Root of 1/81 by Prime Factorization Method

The prime factorization of a number involves expressing it as a product of its prime factors. Let us look at how 1/81 is broken down into its prime factors:

Step 1: Finding the prime factors of 81 Breaking it down, we get 3 × 3 × 3 × 3 = 3^4.

Step 2: Since 1 is a perfect square, it remains as is: 1 = 1^2.

Step 3: Pair the prime factors of the denominator. We can pair the factors into (3^2) × (3^2).

Step 4: The square root of each pair is 3, so the square root of the denominator is 3 × 3 = 9.

Step 5: Therefore, the square root of 1/81 is 1/9.

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Square Root of 1/81 by Long Division Method

The long division method is commonly used for non-perfect square numbers, but it can also verify your result for perfect squares.

Step 1: Consider the numerator and denominator separately. The square root of 1 is 1.

Step 2: Apply the long division method for 81 to confirm that its square root is 9.

Step 3: Therefore, the square root of 1/81 is 1/9.

Common Mistakes and How to Avoid Them in the Square Root of 1/81

Students often make mistakes while finding square roots, such as forgetting about the negative square root or confusing it with cube roots. Let's explore some common errors and how to avoid them.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/81)?

Okay, lets begin

The area of the square is 1/81 square units.

Explanation

The area of the square = side^2.

The side length is given as √(1/81).

Area of the square = side^2 = (1/9) × (1/9) = 1/81.

Therefore, the area of the square box is 1/81 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1/81 square meters is built; if each of the sides is √(1/81), what will be the square meters of half of the building?

Okay, lets begin

1/162 square meters

Explanation

We can divide the given area by 2 as the building is square-shaped.

Dividing 1/81 by 2 = 1/162.

So half of the building measures 1/162 square meters.

Well explained 👍

Problem 3

Calculate √(1/81) × 5.

Okay, lets begin

5/9

Explanation

The first step is to find the square root of 1/81, which is 1/9. The second step is to multiply 1/9 by 5. So (1/9) × 5 = 5/9.

Well explained 👍

Problem 4

What will be the square root of (1/81 + 8)?

Okay, lets begin

The square root is approximately 2.833.

Explanation

To find the square root, we need to find the sum of (1/81 + 8).

1/81 + 8 = 8.012345.

Then the square root of 8.012345 is approximately 2.833.

Therefore, the square root of (1/81 + 8) is approximately ±2.833.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(1/81) units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 76.222 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√(1/81) + 38) = 2 × (1/9 + 38) = 2 × (0.1111 + 38) = 2 × 38.1111 = 76.222 units.

Well explained 👍

FAQ on Square Root of 1/81

1.What is √(1/81) in its simplest form?

The prime factorization of 81 is 3 × 3 × 3 × 3, so the simplest form of √(1/81) = 1/9.

2.Mention the factors of 1/81.

The factors of 1/81 are 1/81 and 1 since 1/81 is a fraction.

3.Calculate the square of 1/81.

We get the square of 1/81 by multiplying the number by itself, that is (1/81) × (1/81) = 1/6561.

4.Is 1/81 a prime number?

5.1/81 is divisible by?

1/81 is a fraction and not divisible by whole numbers other than itself.

Important Glossaries for the Square Root of 1/81

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
  • Perfect square: A number that can be expressed as the square of an integer. Example: 9 is a perfect square since it can be written as 3^2.
  • Fraction: A numerical quantity that is not a whole number, represented by two numbers showing parts of a whole. Example: 1/2, 3/4.
  • Divisor: A number by which another number is to be divided. Example: In 12 ÷ 3 = 4, the divisor 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.