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130 LearnersLast updated on December 15, 2025
Square Root of 9/49
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 such as vehicle design, finance, etc. Here, we will discuss the square root of 9/49.
What is the Square Root of 9/49?
The square root is the inverse of the square of the number.
9/49 can be simplified as a fraction of perfect squares.
The square root of 9/49 is expressed in both radical and exponential form.
In radical form, it is expressed as √(9/49), whereas in exponential form it is (9/49)(1/2).
Since both 9 and 49 are perfect squares, √(9/49) = √9 / √49 = 3/7, 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 9/49
For fractions that are perfect squares, the prime factorization method is effective.
However, for fractions that are not perfect squares, methods like the long-division method and approximation method are used.
For 9/49, we will use the prime factorization method.
Let's explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 9/49 by Prime Factorization Method
The product of prime factors is the prime factorization of a number.
Let us look at how 9/49 is broken down into its prime factors.
Step 1: Finding the prime factors of 9 and 49
Breaking it down, we get 9 = 3 x 3 and 49 = 7 x 7.
Step 2: Now that we have found the prime factors of 9/49, we can take the square root of each. Since both 9 and 49 are perfect squares, we have: √(9/49) = √9 / √49 = 3/7
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Square Root of 9/49 by Long Division Method
The long-division method is useful for finding the square roots of non-perfect square numbers.
However, since 9/49 is a fraction of perfect squares, the long-division method is not necessary here.
Square Root of 9/49 by Approximation Method
The approximation method is used for finding the square roots of numbers that are not perfect squares.
Since 9/49 is a fraction of perfect squares, we do not need to use this method for this fraction.
Common Mistakes and How to Avoid Them in the Square Root of 9/49
Students often make mistakes when finding square roots, such as forgetting about the negative square root or incorrectly simplifying fractions.
Let's look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important for students to remember that a number has both positive and negative square roots.
However, we usually take only the positive square root unless specified otherwise.
For example, √(9/49) = 3/7, but there is also -3/7.
Mistake 2
Not adding the square root symbol in proper places
Misusing the square root symbol is a common mistake.
It is important to simplify numbers inside the square root correctly before proceeding.
For example, √(9/49 + 4/49) is not the same as √(9/49) + √(4/49).
Mistake 3
Not finding the correct value of a non-perfect square
To avoid mistakes, students should simplify the numbers inside the square root.
For example, √50 = 7 is wrong; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube roots and square roots.
For example, √50 and โ50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long-division method involves many steps.
Students may skip a step, leading to incorrect results.
Although this method is not needed for 9/49, it is useful for non-perfect squares.
Square Root of 9/49 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ(9/49)?
The area of the square is 9/49 square units.
Explanation
The area of the square = side².
The side length is given as √(9/49).
Area of the square = (√(9/49))² = 9/49.
Therefore, the area of the square box is 9/49 square units.
Problem 2
A rectangular garden has an area of 9/49 square meters. If its width is โ(9/49), what is the length?
The length of the garden is 1 meter.
Explanation
Area = length × width. Given the width is √(9/49) = 3/7, and the area is 9/49.
Length = Area / Width = (9/49) / (3/7) = 1 meter.
Problem 3
Calculate โ(9/49) ร 7.
The result is 3.
Explanation
First, find the square root of 9/49, which is 3/7.
Then, multiply 3/7 by 7. 3/7 × 7 = 3.
Problem 4
What will be the square root of (9/49 + 25/49)?
The square root is 4/7.
Explanation
First, find the sum of (9/49 + 25/49) = 34/49.
Then, find the square root of 34/49, which is √34/7.
This is approximately 4/7.
Problem 5
Find the perimeter of a square if its side length is โ(9/49) units.
The perimeter of the square is 12/7 units.
Explanation
Perimeter of a square = 4 × side.
Side length is √(9/49) = 3/7.
Perimeter = 4 × (3/7) = 12/7 units.
FAQ on Square Root of 9/49
1.What is โ(9/49) in its simplest form?
2.Mention the factors of 9 and 49.
3.Calculate the square of 9/49.
4.Is 9/49 a prime number?
5.9/49 is divisible by?
Important Glossaries for the Square Root of 9/49
- Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse is the square root, √16 = 4.
- Rational number: A rational number is a number that can be expressed in the form of p/q, where p and q are integers, and q ≠ 0.
- Prime factorization: This is the process of expressing a number as a product of its prime factors.
- Fraction: A fraction represents a part of a whole number and is expressed as a ratio of two integers, such as 1/2 or 3/4.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 9 and 49 are perfect squares.
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.
