103 LearnersLast updated on May 26th, 2025
Square Root of 2/9
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.
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.
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, √(4/9) = 2/3, there is also -2/3 which should not be forgotten.
Square Root of 2/9 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(4/9)?
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.
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?
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.
Problem 3
Calculate √(2/9) x 5.
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.
Problem 4
What will be the square root of (1/9 + 1/36)?
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.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(1/9) units and the width ‘w’ is 3 units.
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.
FAQ on Square Root of 2/9
1.What is √(2/9) in its simplest form?
2.Mention the factors of 9.
3.Calculate the square of 2/9.
4.Is 2/9 a prime number?
5.2/9 is divisible by?
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.
