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128 LearnersLast updated on December 15, 2025
Square Root of 64/49
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.
Square Root of 64/49 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ(81/16)?
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.
Problem 2
A square-shaped building measuring 64/49 square meters is built; if each of the sides is โ(64/49), what will be the square meters of half of the building?
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.
Problem 3
Calculate โ(64/49) x 5.
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
Problem 4
What will be the square root of (49/64 + 15/64)?
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.
Problem 5
Find the perimeter of the rectangle if its length โlโ is โ(81/16) units and the width โwโ is 3 units.
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.
FAQ on Square Root of 64/49
1.What is โ(64/49) in its simplest form?
2.Mention the factors of 64 and 49.
3.Calculate the square of 64/49.
4.Is 64/49 a rational number?
5.Is 64 a perfect square?
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.
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.
