Square Root of 49/144
2026-02-28 12:06 Diff
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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 49/144.

What is the Square Root of 49/144?

The square root is the inverse of the square of the number.

The fraction 49/144 is a perfect square, as both the numerator and denominator are perfect squares.

The square root of 49/144 is expressed in both radical and exponential form.

In the radical form, it is expressed as √(49/144), whereas (49/144)(1/2) in exponential form. √(49/144) = 7/12, 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 49/144

The prime factorization method can be used for perfect square numbers.

For fractions that are perfect squares, we can find the square root of both the numerator and the denominator separately.

Let us now learn the following methods:

  • Prime factorization method
     
  • Simplification method

Square Root of 49/144 by Prime Factorization Method

The product of prime factors is the prime factorization of a number.

Now, let us look at how 49 and 144 are broken down into their prime factors:

Step 1: Finding the prime factors of 49 and 144. - 49 = 7 x 7 = 7² - 144 = 2 x 2 x 2 x 2 x 3 x 3 = 2⁴ x 3²

Step 2: Since both 49 and 144 are perfect squares, we can directly find the square roots: - √49 = 7 - √144 = 12

Therefore, √(49/144) = 7/12.

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Square Root of 49/144 by Simplification Method

The simplification method is a straightforward approach to finding the square roots of fractions.

Let us learn how to find the square root of 49/144 using simplification:

Step 1: Identify the perfect squares in the numerator and the denominator. - √49 = 7 - √144 = 12

Step 2: Simplify the square root of the fraction by taking the square root of the numerator and the denominator separately: - √(49/144) = 7/12

Thus, the square root of 49/144 is 7/12.

Common Mistakes and How to Avoid Them in the Square Root of 49/144

Students often make mistakes while finding the square root of fractions, such as not simplifying the fraction first or incorrectly applying the square root separately to the numerator and denominator.

Let us look at a few common mistakes and how to avoid them.

Problem 1

Can you help Max find the side length of a square if its area is 49/144 square units?

Okay, lets begin

The side length of the square is 7/12 units.

Explanation

The area of the square = side².

The area is given as 49/144 square units.

Therefore, side = √(49/144) = 7/12.

Thus, the side length of the square is 7/12 units.

Well explained 👍

Problem 2

A rectangular garden has an area of 49/144 square meters. If the length is √49 meters, what is the width of the garden?

Okay, lets begin

The width of the garden is 1/12 meters.

Explanation

The area of the rectangle = length × width.

Given, length = √49 = 7 meters and

area = 49/144 square meters.

Width = Area / Length

= (49/144) / 7

= 1/12 meters.

Well explained 👍

Problem 3

Calculate 5 × √(49/144).

Okay, lets begin

The result is 35/12.

Explanation

First, find the square root of 49/144, which is 7/12.

Then, multiply by 5:

5 × 7/12 = 35/12.

Well explained 👍

Problem 4

What is the square root of (49 + 95/144)?

Okay, lets begin

The square root is 13/12.

Explanation

First, find the sum: 49 + 95/144

= 49/1 + 95/144

= 7201/144.

Then, find the square root:

√(7201/144) = 13/12.

Well explained 👍

Problem 5

A square plot measures 49/144 square meters in area. What is the perimeter of the plot?

Okay, lets begin

The perimeter of the plot is 28/12 meters, or 7/3 meters.

Explanation

Side of the square = √(49/144) = 7/12.

Perimeter of the square = 4 × side

= 4 × 7/12

= 28/12 meters or 7/3 meters.

Well explained 👍

FAQ on Square Root of 49/144

1.What is √(49/144) in its simplest form?

The simplest form of √(49/144) is 7/12.

2.Mention the factors of 49 and 144.

Factors of 49 are 1, 7, and 49. Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

3.Calculate the square of 49/144.

The square of 49/144 is (49/144)² = 2401/20736.

4.Is 49/144 a rational number?

Yes, 49/144 is a rational number because it can be expressed as a ratio of two integers.

5.Is (49/144) a perfect square?

Yes, 49/144 is a perfect square because both the numerator and denominator are perfect squares.

Important Glossaries for the Square Root of 49/144

  • Square root: The square root is the inverse operation of squaring a number. For example, the square root of 16 is 4 because 4² = 16.
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 49 and 144 are perfect squares.
  • Rational number: A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.
  • Fraction: A fraction represents a part of a whole or any number of equal parts. It is expressed as p/q, where p and q are integers, and q ≠ 0.
  • Simplification: The process of reducing a mathematical expression to its simplest form. In fractions, it involves finding and dividing by the greatest common divisor of the numerator and denominator.

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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.