Square Root of 16/25
2026-02-28 06:04 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-16/25

318 Learners

Last updated on August 5, 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.

What is 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.

Finding the Square Root of 16/25

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:

  • Direct calculation method
     
  • Fraction simplification method

Square Root of 16/25 by Direct Calculation Method

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

Explore Our Programs

Square Root of 16/25 by Fraction Simplification Method

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

Applications of the Square Root of 16/25

The square root of 16/25, which is 4/5, can be applied in various situations such as:

  • Calculating the dimensions of a scaled model when given in fractional form.
     
  • Converting units when the conversion factor is a fraction.
     
  • Financial calculations involving percentage changes expressed as fractions.

Common Mistakes and How to Avoid Them in the Square Root of 16/25

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.

Problem 1

Can you help Max find the side length of a square box if its area is 16/25 square units?

Okay, lets begin

The side length of the square box is 4/5 units.

Explanation

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.

Well explained 👍

Problem 2

A rectangle has an area of 16/25 square meters. If its length is 4/5 meters, what is its width?

Okay, lets begin

The width of the rectangle is 1 meter.

Explanation

Area of a rectangle = length × width.

Given area = 16/25 and length = 4/5, width = area/length = (16/25) / (4/5) = 1.

Well explained 👍

Problem 3

Calculate (16/25)^(1/2) × 10.

Okay, lets begin

8

Explanation

First, find the square root of 16/25, which is 4/5. Then, multiply by 10: (4/5) × 10 = 8.

Well explained 👍

Problem 4

What will be the square root of (9/16) + (16/25)?

Okay, lets begin

The square root is 49/20 or 2.45

Explanation

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.

Well explained 👍

Problem 5

Find the hypotenuse of a right triangle if one leg is 3/5 units and the other leg is 4/5 units.

Okay, lets begin

The hypotenuse is 1 unit.

Explanation

Using the Pythagorean theorem: hypotenuse² = (3/5)² + (4/5)² = 9/25 + 16/25 = 25/25 = 1. Therefore, the hypotenuse = √1 = 1 unit.

Well explained 👍

FAQ on Square Root of 16/25

1.What is √(16/25) in its simplest form?

The simplest form of √(16/25) = 4/5.

2.What is the square of 16/25?

The square of 16/25 is (16/25) × (16/25) = 256/625.

3.Is 16/25 a rational number?

Yes, 16/25 is a rational number because it can be expressed as a fraction of two integers.

4.How do you simplify the square root of a fraction?

To simplify the square root of a fraction, take the square root of the numerator and the square root of the denominator separately.

5.Is 16/25 a perfect square?

Yes, 16/25 is a perfect square because its square root is a rational number, 4/5.

Important Glossaries for the Square Root of 16/25

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √16 = 4.
  • Rational number: A rational number is a number that can be expressed as the quotient or fraction of two integers.
  • Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 and 25 are perfect squares.
  • Fraction: A fraction represents a part of a whole or a division of quantities. It consists of a numerator and a denominator.
  • Principal square root: The principal square root is the non-negative square root of a number. For example, the principal square root of 9 is 3.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.