Square Root of 49/25
2026-02-28 12:07 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-49-by-25

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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. Square roots are used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 49/25.

What is the Square Root of 49/25?

The square root is the inverse of the square of the number. 49/25 is a perfect square fraction.

The square root of 49/25 is expressed in both radical and exponential form.

In the radical form, it is expressed as √(49/25), whereas (49/25)(1/2) is the exponential form. √(49/25) = 7/5, 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 49/25

To find the square root of a perfect square fraction, we take the square root of the numerator and the denominator separately.

Let's explore this method:

Square root of the numerator: √49 = 7

Square root of the denominator: √25 = 5

Thus, the square root of 49/25 is 7/5.

Square Root of 49/25 by Prime Factorization Method

The prime factorization method can also be used to find square roots of perfect squares.

Let's see how 49/25 can be broken down:

Step 1: Prime factorization of the numerator and the denominator - 49 = 7 x 7 - 25 = 5 x 5

Step 2: Taking the square root of each part - √49 = 7 - √25 = 5

Therefore, the square root of 49/25 is 7/5.

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Square Root of 49/25 by Long Division Method

The long division method is not needed for perfect square fractions like 49/25, as the square roots of the numerator and the denominator can be easily calculated.

However, if you wish to use this method, you would start by dividing the numerator and denominator separately and finding their square roots:

 √49 = 7 using division

√25 = 5 using division

So, the square root of 49/25 is 7/5.

Square Root of 49/25 by Approximation Method

The approximation method is typically used for non-perfect square numbers.

For perfect square fractions, direct calculation is more efficient:

Step 1: Identify perfect square numbers

√49 = 7,

 √25 = 5,

Thus, the square root of 49/25 is directly 7/5.

Common Mistakes and How to Avoid Them in the Square Root of 49/25

Students might make mistakes while finding square roots, such as forgetting the properties of fractions or miscalculating individual square roots.

Let us explore some common mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(49/25)?

Okay, lets begin

The area of the square is 49/25 square units.

Explanation

The area of the square = side2.

The side length is given as √(49/25).

Area of the square = (√(49/25))2 = (7/5) x (7/5) = 49/25.

Therefore, the area of the square box is 49/25 square units.

Well explained 👍

Problem 2

A square field has an area of 49/25 square units. What is the side length of the field?

Okay, lets begin

The side length of the field is 7/5 units.

Explanation

If the area of a square is 49/25, then the side length is the square root of 49/25.

√(49/25) = 7/5.

So, the side length of the field is 7/5 units.

Well explained 👍

Problem 3

Calculate 2 x √(49/25).

Okay, lets begin

2 x √(49/25) = 14/5

Explanation

First, find the square root of 49/25, which is 7/5.

Then, multiply 7/5 by 2.

So, 2 x (7/5) = 14/5.

Well explained 👍

Problem 4

What is the square root of (49/25) x 25?

Okay, lets begin

The square root is 7.

Explanation

First, simplify (49/25) x 25 = 49.

Then, the square root of 49 is 7.

Therefore, the square root is ±7.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √(49/25) units and the width 'w' is 10 units.

Okay, lets begin

The perimeter of the rectangle is 24 units.

Explanation

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

Perimeter = 2 × (√(49/25) + 10)

= 2 × (7/5 + 10).

Convert 10 to a fraction:

10 = 50/5.

So, Perimeter = 2 × (7/5 + 50/5)

= 2 × (57/5)

= 114/5

= 22.8 units.

Well explained 👍

FAQ on Square Root of 49/25

1.What is √(49/25) in its simplest form?

The simplest form of √(49/25) is 7/5, as both the numerator (49) and the denominator (25) are perfect squares.

2.How do you find the square root of a fraction?

To find the square root of a fraction, find the square root of the numerator and the square root of the denominator separately. Then, divide the two results.

3.Is 49/25 a rational number?

Yes, 49/25 is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers.

4.What is the decimal form of √(49/25)?

The decimal form of √(49/25) is 1.4, as 7 divided by 5 equals 1.4.

5.Is √(49/25) greater than 1?

Yes, √(49/25) is greater than 1 because 7/5 is equal to 1.4, which is greater than 1.

Important Glossaries for the Square Root of 49/25

  • Square root: A square root is the inverse of a square. For example, if 42 = 16, then the square root of 16 is √16 = 4.
  • Rational number: A rational number can be expressed as a fraction p/q, where p and q are integers, and q is not zero.
  • Perfect square: A number is a perfect square if it can be expressed as the square of an integer. For example, 49 is a perfect square because it is 72.
  • Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator.
  • Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, such as 1.4.

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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.