131 LearnersLast updated on May 26th, 2025
Square Root of 64/25
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as architecture, statistics, and mathematics. Here, we will discuss the square root of 64/25.
What is the Square Root of 64/25?
The square root is the inverse operation of squaring a number. The fraction 64/25 is a perfect square because both the numerator and denominator are perfect squares. The square root of 64/25 is expressed in both radical and exponential forms. In radical form, it is expressed as √(64/25), whereas in exponential form it is (64/25)^(1/2). √(64/25) = 8/5, 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 64/25
The prime factorization method can be used for perfect square numbers. For fractions that are perfect squares, we can directly find the square root of the numerator and the denominator. Let us now learn the following methods:
- Prime factorization method
- Direct square root method
Square Root of 64/25 by Prime Factorization Method
The prime factorization of a number involves expressing it as a product of its prime factors. Let's look at how 64/25 can be expressed:
Step 1: Finding the prime factors of 64 and 25.
64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6
25 = 5 x 5 = 5^2
Step 2: Taking the square root of each, we have: √64 = √(2^6) = 2^3 = 8 √25 = √(5^2) = 5
Step 3: Therefore, the square root of 64/25 is 8/5.
Square Root of 64/25 by Direct Method
The direct method involves finding the square root of both the numerator and the denominator separately:
Step 1: Find the square root of 64, which is 8, since 8 x 8 = 64.
Step 2: Find the square root of 25, which is 5, since 5 x 5 = 25.
Step 3: Therefore, the square root of 64/25 is 8/5.
Square Root of 64/25 by Approximation Method
The approximation method generally applies to non-perfect squares, but since 64/25 is a perfect square, we can confirm our result through approximation:
Step 1: Recognize that 64/25 is close to 2.56.
Step 2: √(2.56) is approximately 1.6, which is close to 8/5 = 1.6.
Common Mistakes and How to Avoid Them in the Square Root of 64/25
Students often make mistakes while finding the square root, such as ignoring the negative square root or not simplifying fractions properly. Let's explore a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
Remember, every positive number has two square roots: one positive and one negative. However, we typically consider only the principal (positive) square root.
For example, √(64/25) = ±8/5, but we usually refer to the positive root.
Mistake 2
Not simplifying fractions properly
Ensure that fractions are simplified before finding their square roots.
For instance, simplifying 64/25 directly to 8/5 before taking the square root can prevent errors.
Mistake 3
Confusing the square root with division
Avoid confusing square roots with division.
For example, √(64/25) = 8/5 is not the same as dividing 64 by 25.
Mistake 4
Mistaking square root symbols
Be clear about the application of square root symbols. Ensure the entire fraction is under the square root, i.e., √(64/25), not √64/25 or 64/√25.
Mistake 5
Errors in prime factorization
Mistakes in the prime factorization process can lead to incorrect results. Double-check each factorization step to ensure accuracy.
Square Root of 64/25 Examples
Problem 1
Can you help Mia find the side length of a square if its area is 64/25 square units?
The side length of the square is 8/5 units.
Explanation
The side length of a square is the square root of its area.
Area = 64/25
Side length = √(64/25) = 8/5 units.
Problem 2
A square garden has an area of 64/25 square meters. What is the perimeter?
The perimeter of the square is 32/5 meters.
Explanation
Perimeter of a square = 4 × side length
Side length = 8/5 meters
Perimeter = 4 × 8/5 = 32/5 meters
Problem 3
Calculate √(64/25) × 3.
The result is 24/5.
Explanation
First, find the square root of 64/25, which is 8/5.
Then multiply by 3: (8/5) × 3 = 24/5
Problem 4
If a rectangle has a length of √(64/25) and a width of 10/3, what is its area?
The area of the rectangle is 80/15 or simplified to 16/3 square units.
Explanation
Area = length × width Length = 8/5, width = 10/3
Area = (8/5) × (10/3) = 80/15 = 16/3 square units
Problem 5
Find the width of a rectangle if its length is 8/5 and perimeter is 34/5.
The width of the rectangle is 9/5 units.
Explanation
Perimeter of a rectangle = 2 × (length + width) 34/5 = 2 × (8/5 + width) 17/5 = 8/5 + width width = 17/5 - 8/5 = 9/5 units
FAQ on Square Root of 64/25
1.What is √(64/25) in its simplest form?
2.Is 64/25 a perfect square?
3.Calculate the square of 64/25.
4.Is 64/25 a rational number?
5.What is the decimal equivalent of 64/25?
Important Glossaries for the Square Root of 64/25
- Square root: A square root is the inverse of squaring a number. For example, the square root of 16 is 4 because 4² = 16.
- Rational number: A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero.
- Perfect square: A perfect square is a number that has an integer as its square root. For example, 9 is a perfect square because its square root is 3.
- Fraction: A fraction consists of a numerator and a denominator, representing a part of a whole. For example, 3/4 is a fraction.
- Perimeter: The perimeter is the total distance around the edge of a two-dimensional shape, such as a rectangle or square.
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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.
