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 vehicle design, finance, etc. Here, we will discuss the square root of 16/25.
The square root is the inverse operation of squaring a number. The number 16/25 is a perfect square fraction. The square root of 16/25 can be expressed in both radical and fractional form. In radical form, it is expressed as √(16/25), whereas in fractional form it is (16/25)^(1/2). The square root of 16/25 is 4/5, 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.
To find the square root of a perfect square fraction, we can take the square root of the numerator and the square root of the denominator separately. Let's learn the following methods:
The direct calculation method involves taking the square root of both the numerator and the denominator.
Step 1: Find the square root of the numerator, 16. √16 = 4
Step 2: Find the square root of the denominator, 25. √25 = 5
Step 3: Combine the results as a fraction. So, √(16/25) = 4/5
The fraction simplification method involves simplifying the fraction by taking the square root of both the numerator and the denominator.
Step 1: Identify the perfect squares in the fraction 16/25. - The numerator 16 is a perfect square of 4. - The denominator 25 is a perfect square of 5.
Step 2: Express the fraction as the product of its square roots. √(16/25) = √16 / √25
Step 3: Simplify the expression. √16 = 4 and √25 = 5 Therefore, √(16/25) = 4/5
The square root of 16/25, which is 4/5, can be applied in various situations such as:
Students often make mistakes while finding square roots of fractions, such as ignoring the need to simplify both the numerator and the denominator. Let's look at some common mistakes in detail.
Can you help Max find the side length of a square box if its area is 16/25 square units?
The side length of the square box is 4/5 units.
The side length of a square is the square root of its area. Given that the area is 16/25, the side length = √(16/25) = 4/5.
A rectangle has an area of 16/25 square meters. If its length is 4/5 meters, what is its width?
The width of the rectangle is 1 meter.
Area of a rectangle = length × width.
Given area = 16/25 and length = 4/5, width = area/length = (16/25) / (4/5) = 1.
Calculate (16/25)^(1/2) × 10.
8
First, find the square root of 16/25, which is 4/5. Then, multiply by 10: (4/5) × 10 = 8.
What will be the square root of (9/16) + (16/25)?
The square root is 49/20 or 2.45
First, find the sum of (9/16) + (16/25) = (225/400) + (256/400) = 481/400. The square root of 481/400 is approximately 2.45.
Find the hypotenuse of a right triangle if one leg is 3/5 units and the other leg is 4/5 units.
The hypotenuse is 1 unit.
Using the Pythagorean theorem: hypotenuse² = (3/5)² + (4/5)² = 9/25 + 16/25 = 25/25 = 1. Therefore, the hypotenuse = √1 = 1 unit.
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.
: He loves to play the quiz with kids through algebra to make kids love it.