Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
The side length of a square is the square root of its area.
Area = 64/25
Side length = √(64/25) = 8/5 units.
A square garden has an area of 64/25 square meters. What is the perimeter?
The perimeter of the square is 32/5 meters.
Perimeter of a square = 4 × side length
Side length = 8/5 meters
Perimeter = 4 × 8/5 = 32/5 meters
Calculate √(64/25) × 3.
The result is 24/5.
First, find the square root of 64/25, which is 8/5.
Then multiply by 3: (8/5) × 3 = 24/5
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.
Area = length × width Length = 8/5, width = 10/3
Area = (8/5) × (10/3) = 80/15 = 16/3 square units
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.
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
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.
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