Square Root of 49/9
2026-02-28 06:04 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-49/9

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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 fields such as vehicle design and finance. Here, we will discuss the square root of 49/9.

What is the Square Root of 49/9?

The square root is the inverse of the square of the number. 49/9 is a perfect square fraction. The square root of 49/9 is expressed in both radical and exponential form. In radical form, it is expressed as √(49/9), whereas in exponential form it is expressed as (49/9)^(1/2). √(49/9) = 7/3, 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 49/9

For perfect square numbers, the prime factorization method can be used. However, since 49/9 is a simple fraction of perfect squares, we can directly find its square root. Let us now learn the following methods:

  • Direct method for perfect square fractions
  • Verification by multiplication

Square Root of 49/9 by Direct Method

Since 49 and 9 are both perfect squares, we can find the square root of each separately.

Step 1: Find the square root of the numerator (49). √49 = 7

Step 2: Find the square root of the denominator (9). √9 = 3 Therefore, √(49/9) = 7/3.

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Square Root of 49/9 by Verification

We can verify our result by squaring the outcome of the square root to check if it equals the original number.

Step 1: Square the result obtained from the direct method. (7/3)² = 49/9

Step 2: Compare it with the original fraction. Since (7/3)² equals 49/9, our result is verified.

Common Mistakes and How to Avoid Them in the Square Root of 49/9

Students often make mistakes while finding the square root, such as confusing the process for non-perfect square numbers or forgetting about negative square roots. Let us look at a few common mistakes in detail.

Common Mistakes and How to Avoid Them in the Square Root of 49/9

Students often make mistakes while finding the square root, such as confusing the process for non-perfect square numbers or forgetting about negative square roots. Let us 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 √(49/9)?

Okay, lets begin

The area of the square is 49/9 square units.

Explanation

The area of the square = side².

The side length is given as √(49/9).

Area of the square = (7/3) × (7/3) = 49/9.

Therefore, the area of the square box is 49/9 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 49/9 square feet is built; if each of the sides is √(49/9), what will be the square feet of half of the building?

Okay, lets begin

24.5/9 square feet

Explanation

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

Dividing 49/9 by 2 = 24.5/9.

So half of the building measures 24.5/9 square feet.

Well explained 👍

Problem 3

Calculate √(49/9) × 5.

Okay, lets begin

35/3

Explanation

The first step is to find the square root of 49/9, which is 7/3.

The second step is to multiply 7/3 by 5.

So (7/3) × 5 = 35/3.

Well explained 👍

Problem 4

What will be the square root of (49/9 + 1)?

Okay, lets begin

The square root is 4/3.

Explanation

To find the square root, we need to find the sum of (49/9 + 1). 49/9 + 9/9 = 58/9. √(58/9) is not an integer, but if simplified, it falls between 2 and 3.

Since 58 is close to 64, which is a perfect square, we can approximate it as √64/9 = 8/3.

Therefore, the square root of (49/9 + 1) is approximately 4/3.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(49/9) units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 84/3 + 76 units.

Explanation

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

Perimeter = 2 × (7/3 + 38) = 2 × (84/3 + 114/3) = 2 × 198/3 = 396/3 = 132 units.

Well explained 👍

FAQ on Square Root of 49/9

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

The simplest form of √(49/9) is 7/3 because both the numerator and the denominator are perfect squares.

2.Mention the factors of 49/9.

Factors of 49/9 are the factors of 49, which are 1, 7, 49, and 9, which are 1, 3, and 9.

3.Calculate the square of 49/9.

We get the square of 49/9 by multiplying the number by itself, that is (49/9) × (49/9) = 2401/81.

4.Is 49/9 a rational number?

Yes, 49/9 is a rational number because it can be expressed as a fraction of two integers.

5.49/9 is divisible by?

49/9 as a fraction is not divisible by integers to yield another integer. However, its components 49 and 9 are divisible by their respective factors.

Important Glossaries for the Square Root of 49/9

  • Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, which is √16 = 4.
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 49 is a perfect square because 7² = 49.
  • Fraction: A fraction is a way to represent a part of a whole, expressed as a ratio of two integers, such as 1/2 or 49/9.
  • Approximation: An approximation is a value or number that is close to but not exactly equal to the actual value, often used when exact values are difficult to obtain.

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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.