Square Root of 2/9
2026-02-28 10:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2-by-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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 2/9.

What is the Square Root of 2/9?

The square root is the inverse of the square of a number. 2/9 is not a perfect square. The square root of 2/9 is expressed in both radical and exponential form. In the radical form, it is expressed as √(2/9), whereas (2/9)^(1/2) in exponential form. √(2/9) = √2/√9 = √2/3, 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 2/9

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 2/9 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 2/9 is broken down into its prime factors:

Step 1: Finding the prime factors of 2 and 9. Breaking it down, we get 2 as 2 and 9 as 3 x 3: 2 and 3^2.

Step 2: Now we found out the prime factors of 2/9. The second step is to make pairs of those prime factors. Since 2/9 is not a perfect square, calculating the square root of 2/9 using prime factorization involves taking the square root of the numerator and the denominator separately.

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Square Root of 2/9 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we can check by dividing 2 by 9 first, and then finding the square root. Let us now learn how to find the square root using the long division method, step by step:

Step 1: Divide 2 by 9 to get 0.222.

Step 2: Find the square root of 0.222... using the long division method.

Step 3: Group the digits in pairs from the decimal point, i.e., 0.22 | 20.

Step 4: Find the largest number whose square is less than or equal to 2.00, which is 1. The divisor becomes 1.

Step 5: Subtract 1 from 2.00 to get 1.00, then bring down the next pair to get 100.

Step 6: Double the current divisor (1) to get 2, and find a digit n such that 2n × n is less than or equal to 100. The digit is 4 because 24 × 4 = 96.

Step 7: Subtract 96 from 100 to get 4, then bring down the next pair to get 400.

Step 8: Continue this process until you get the desired precision.

Square Root of 2/9 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 2/9 using the approximation method.

Step 1: Approximate the square root of 2/9 by estimating the square roots of the numerator and denominator. √2 is approximately 1.414 and √9 is exactly 3.

Step 2: Divide the approximate square root of the numerator by the square root of the denominator: 1.414/3 ≈ 0.471

Step 3: This approximate value is the square root of 2/9, i.e., 0.471.

Common Mistakes and How to Avoid Them in the Square Root of 2/9

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods. 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 √(4/9)?

Okay, lets begin

The area of the square is 4/9 or approximately 0.444 square units.

Explanation

The area of the square = side².

The side length is given as √(4/9).

Area of the square = (√(4/9))²

= 4/9.

Therefore, the area of the square box is 4/9 or approximately 0.444 square units.

Well explained 👍

Problem 2

A square-shaped garden measuring 2/9 square meters is built; if each of the sides is √(2/9), what will be the square meters of half of the garden?

Okay, lets begin

1/9 square meter

Explanation

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

Dividing 2/9 by 2 = 1/9.

So half of the garden measures 1/9 square meter.

Well explained 👍

Problem 3

Calculate √(2/9) x 5.

Okay, lets begin

Approximately 2.355

Explanation

The first step is to find the square root of 2/9 which is approximately 0.471, the second step is to multiply 0.471 with 5.

So 0.471 × 5 ≈ 2.355.

Well explained 👍

Problem 4

What will be the square root of (1/9 + 1/36)?

Okay, lets begin

The square root is approximately 0.333

Explanation

To find the square root, we need to find the sum of (1/9 + 1/36).

1/9 + 1/36 = 4/36 + 1/36 = 5/36, and then √(5/36) ≈ 0.333.

Therefore, the square root of (1/9 + 1/36) is approximately 0.333.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(1/9) units and the width ‘w’ is 3 units.

Okay, lets begin

We find the perimeter of the rectangle as approximately 6.67 units.

Explanation

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

Perimeter = 2 × (√(1/9) + 3)

= 2 × (1/3 + 3)

= 2 × 3.333

= 6.67 units.

Well explained 👍

FAQ on Square Root of 2/9

1.What is √(2/9) in its simplest form?

The prime factorization of 2 is 2 and 9 is 3 x 3, so the simplest form of √(2/9) is √2/3.

2.Mention the factors of 9.

Factors of 9 are 1, 3, and 9.

3.Calculate the square of 2/9.

We get the square of 2/9 by multiplying the number by itself, that is (2/9) x (2/9) = 4/81.

4.Is 2/9 a prime number?

5.2/9 is divisible by?

2/9 is a fraction, so it is not divisible by integers in the usual sense.

However, it can be simplified by dividing both the numerator and the denominator by their greatest common factor, which in this case is 1.

Important Glossaries for the Square Root of 2/9

  • Square root: A square root is the inverse operation of squaring a number. For example, 4² = 16, and the inverse operation is the square root: √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 and is expressed as a ratio of two integers, such as 1/2, 3/4, etc.
     
  • Perimeter: The perimeter is the total length of the boundary of a two-dimensional shape. For a rectangle, it is calculated as 2 × (length + width).
     
  • Approximation: Approximation is the process of finding a value that is close enough to the correct answer, usually within a specified range.

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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.