Square Root of 9/49
2026-02-28 12:08 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9-by-49

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Last updated on December 15, 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 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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(9/49)?

Okay, lets begin

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.

Well explained 👍

Problem 2

A rectangular garden has an area of 9/49 square meters. If its width is √(9/49), what is the length?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(9/49) × 7.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (9/49 + 25/49)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of a square if its side length is √(9/49) units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 9/49

1.What is √(9/49) in its simplest form?

Since both 9 and 49 are perfect squares, the simplest form of √(9/49) is 3/7.

2.Mention the factors of 9 and 49.

Factors of 9 are 1, 3, and 9.

Factors of 49 are 1, 7, and 49.

3.Calculate the square of 9/49.

The square of 9/49 is (9/49) × (9/49) = 81/2401.

4.Is 9/49 a prime number?

5.9/49 is divisible by?

9/49 is divisible by 1, 3/7, and 9/49.

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.

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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.