Square Root of 1/9
2026-02-28 06:09 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1/9

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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 various fields like vehicle design, finance, etc. Here, we will discuss the square root of 1/9.

What is the Square Root of 1/9?

The square root is the inverse of the square of the number. 1/9 is a perfect square. The square root of 1/9 is expressed in both radical and exponential form. In radical form, it is expressed as √(1/9), whereas (1/9)^(1/2) in exponential form. √(1/9) = 1/3, 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 1/9

For perfect square numbers like 1/9, we can use direct methods such as simplification. Let us now learn the following methods:

  • Simplification method
  • Using properties of exponents

Square Root of 1/9 by Simplification Method

The simplification method involves expressing the number as a square of a simpler number. Let us look at how 1/9 is simplified:

Step 1: Express 1/9 as a square of a number. 1/9 = (1/3)²

Step 2: Take the square root of both sides. √(1/9) = √((1/3)²)

Step 3: The square root of (1/3)² is 1/3. So, √(1/9) = 1/3.

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Square Root of 1/9 Using Properties of Exponents

Using properties of exponents is an efficient method for finding square roots. Let us learn how to find the square root of 1/9 using this method.

Step 1: Express 1/9 using exponents. 1/9 = (1/3)²

Step 2: Apply the exponent rule (a^m)^(1/n) = a^(m/n). (1/9)^(1/2) = ((1/3)²)^(1/2)

Step 3: Simplify the exponent. = (1/3)^(2/2) = (1/3)^1 = 1/3 Therefore, the square root of 1/9 is 1/3.

Common Mistakes and How to Avoid Them in the Square Root of 1/9

Students often make mistakes while finding the square root, such as forgetting to simplify the fraction. Let's look at a few common mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/9)?

Okay, lets begin

The area of the square is 1/9 square units.

Explanation

The area of the square = side².

The side length is given as √(1/9).

Area of the square = side²

= (1/3) x (1/3)

= 1/9.

Therefore, the area of the square box is 1/9 square units.

Well explained 👍

Problem 2

A square-shaped garden has an area of 1/9 square meters. What is the length of each side?

Okay, lets begin

The length of each side is 1/3 meters.

Explanation

The area of a square is given by side².

Here, side² = 1/9.

To find the side length, take the square root of the area: √(1/9) = 1/3.

So, each side of the garden is 1/3 meters.

Well explained 👍

Problem 3

Calculate √(1/9) x 6.

Okay, lets begin

2

Explanation

The first step is to find the square root of 1/9, which is 1/3.

The second step is to multiply 1/3 by 6. So, (1/3) x 6 = 2.

Well explained 👍

Problem 4

What will be the square root of (1/4 + 1/36)?

Okay, lets begin

The square root is 1/2

Explanation

To find the square root, we first find the sum of (1/4 + 1/36). Convert to a common denominator: (9/36 + 1/36) = 10/36 = 5/18. Then, 5/18 is not a perfect square, so we approximate the square root. The approximate square root of 5/18 is not directly calculable, so further steps would involve approximation methods.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √(1/9) meters and the width 'w' is 1 meter.

Okay, lets begin

The perimeter of the rectangle is 2.67 meters.

Explanation

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

Perimeter = 2 × (√(1/9) + 1)

= 2 × (1/3 + 1)

= 2 × (1.33)

= 2.67 meters.

Well explained 👍

FAQ on Square Root of 1/9

1.What is √(1/9) in its simplest form?

The simplest form of √(1/9) is 1/3. This is because (1/9) = (1/3)², so the square root is 1/3.

2.Is 1/9 a perfect square?

Yes, 1/9 is a perfect square because it can be expressed as (1/3)².

3.What is the square of 1/3?

The square of 1/3 is (1/3) × (1/3) = 1/9.

4.Is √(1/9) a rational number?

Yes, √(1/9) is a rational number because it can be expressed as 1/3, which is a ratio of two integers.

5.Can a square root be negative?

Yes, a square root can be negative.

The square root of a number x is ±√x.

However, when referring to the principal square root, it is the positive value.

In this case, ±√(1/9) = ±1/3.

Important Glossaries for the Square Root of 1/9

  • Square root: A square root is the inverse of squaring. For example, 3² = 9, so the square root of 9 is 3. For 1/9, the square root is 1/3.
     
  • Rational number: A rational number can be expressed as a fraction p/q, where p and q are integers, and q ≠ 0. For example, 1/3 is a rational number.
     
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 9 is a perfect square because it is 3². Similarly, 1/9 is a perfect square because it is (1/3)².
     
  • Exponent: Exponents denote repeated multiplication of a number by itself. For example, (1/3)² means 1/3 multiplied by itself.
     
  • Fraction: A fraction represents a part of a whole and is expressed as the ratio of two numbers, for example, 1/9.

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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.