Square Root of 64/49
2026-02-28 12:04 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-64-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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 64/49.

What is the Square Root of 64/49?

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

64/49 is a rational number and is a perfect square.

The square root of 64/49 can be expressed in both radical and exponential form.

In the radical form, it is expressed as √(64/49), whereas (64/49)(1/2) in the exponential form.

√(64/49) = 8/7, 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 64/49

The prime factorization method can be used for perfect square numbers like 64/49.

However, for illustration, we can use both prime factorization and simplification methods.

Let's explore these methods:

  • Prime factorization method
     
  • Simplification method

Square Root of 64/49 by Prime Factorization Method

The prime factorization involves expressing the numerator and denominator as products of prime numbers.

Step 1: Finding the prime factors of 64 and 49

64 = 2 x 2 x 2 x 2 x 2 x 2 = 26

49 = 7 x 7 = 72

Step 2: Find the square root of both the numerator and the denominator separately. √64 = √(2^6) = 2^3 = 8 √49 = √(7^2) = 7

Step 3: Combine the results √(64/49) = 8/7

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Square Root of 64/49 by Simplification Method

The simplification method is straightforward for perfect square fractions.

Step 1: Split the square root of the fraction into the square roots of the numerator and the denominator. √(64/49) = √64 / √49

Step 2: Calculate the square roots individually. √64 = 8 √49 = 7

Step 3: Divide the results √(64/49) = 8/7

Common Mistakes and How to Avoid Them in the Square Root of 64/49

Students might make mistakes while finding the square root, such as not simplifying correctly or misunderstanding the properties of square roots.

Let's explore some common mistakes and how to avoid them.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(81/16)?

Okay, lets begin

The area of the square is 25.5625 square units.

Explanation

The area of the square = side^2. The side length is given as √(81/16).

Area of the square = √(81/16) x √(81/16) = (9/4) x (9/4) = 81/16 = 25.5625

Therefore, the area of the square box is 25.5625 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 64/49 square meters is built; if each of the sides is √(64/49), what will be the square meters of half of the building?

Okay, lets begin

32/49 square meters

Explanation

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

Dividing 64/49 by 2 = (64/49) / 2 = 32/49

So half of the building measures 32/49 square meters.

Well explained 👍

Problem 3

Calculate √(64/49) x 5.

Okay, lets begin

5.7142857

Explanation

The first step is to find the square root of 64/49, which is 8/7.

The second step is to multiply 8/7 by 5.

So (8/7) x 5 = 40/7 = 5.7142857

Well explained 👍

Problem 4

What will be the square root of (49/64 + 15/64)?

Okay, lets begin

The square root is 0.875

Explanation

To find the square root, we need to find the sum of (49/64 + 15/64). 49/64 + 15/64 = 64/64 = 1, and then √1 = 1.

Therefore, the square root of (49/64 + 15/64) is 1.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(81/16) units and the width ‘w’ is 3 units.

Okay, lets begin

We find the perimeter of the rectangle as 13.5 units.

Explanation

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

Perimeter = 2 × (√(81/16) + 3) = 2 × (9/4 + 3) = 2 × (2.25 + 3) = 2 × 5.25 = 10.5 units.

Well explained 👍

FAQ on Square Root of 64/49

1.What is √(64/49) in its simplest form?

The simplest form of √(64/49) is 8/7 since both the numerator and denominator are perfect squares.

2.Mention the factors of 64 and 49.

Factors of 64 are 1, 2, 4, 8, 16, 32, and 64.

Factors of 49 are 1, 7, and 49.

3.Calculate the square of 64/49.

We get the square of 64/49 by multiplying the number by itself, that is (64/49) x (64/49) = 4096/2401

4.Is 64/49 a rational number?

Yes, 64/49 is a rational number because it can be expressed as a fraction of two integers.

5.Is 64 a perfect square?

Yes, 64 is a perfect square because it can be expressed as 8 x 8.

Important Glossaries for the Square Root of 64/49

  • Square Root: A square root is the inverse of a square. Example: 42 = 16 and the inverse of the square is the square root, that 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 can be expressed as the square of an integer. Example: 64 is a perfect square as it is 8^2.
  • Prime Factorization: Prime factorization is expressing a number as a product of its prime factors. Example: 18 = 2 x 3 x 3.
  • Simplification: Simplification involves reducing a fraction or expression to its simplest form for ease of calculation.

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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.