Square Root of 16/100
2026-02-28 06:07 Diff
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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. Square roots are used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 16/100.

What is the Square Root of 16/100?

The square root is the inverse of the square of the number. 16/100 is a perfect square fraction. The square root of 16/100 can be expressed in both radical and exponential form. In radical form, it is expressed as √(16/100), whereas in exponential form, it is expressed as (16/100)^(1/2). √(16/100) = √(4/10) = 2/10 = 0.2, 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 16/100

The square root of a fraction is found by taking the square root of the numerator and the denominator separately. Let us now learn the method:

Step 1: Find the square root of the numerator (16) and the denominator (100).

Step 2: The square root of 16 is 4, and the square root of 100 is 10.

Step 3: So, the square root of 16/100 is 4/10, which simplifies to 0.2.

Square Root of 16/100 by Prime Factorization Method

Prime factorization can also be used to find the square root of perfect square fractions.

Step 1: Find the prime factors of the numerator and denominator. The prime factors of 16 are 2 x 2 x 2 x 2, and the prime factors of 100 are 2 x 2 x 5 x 5.

Step 2: Pair the prime factors: Numerator: (2 x 2) x (2 x 2) Denominator: (2 x 2) x (5 x 5)

Step 3: Take one factor from each pair: Numerator: 2 x 2 = 4 Denominator: 2 x 5 = 10

Step 4: The square root of 16/100 is 4/10, which simplifies to 0.2.

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Square Root of 16/100 by Long Division Method

The long division method is typically used for non-perfect squares, but it can confirm our results.

Step 1: Express 16/100 as a decimal, which is 0.16.

Step 2: Use long division to find the square root of 0.16.

Step 3: Since 0.16 is a perfect square, the square root is 0.4.

Step 4: Adjust for the initial fraction by dividing by 2 to get 0.2.

Square Root of 16/100 by Approximation Method

Approximation is useful for estimating square roots, especially when a fraction isn't a perfect square.

Step 1: Note that 16/100 is a perfect square, so approximation isn't necessary, but it's helpful to verify.

Step 2: Recognize that √(16/100) is between √(1/100) = 0.1 and √(25/100) = 0.5.

Step 3: Since 16 is a perfect square and so is 100, the exact answer is 0.2.

Common Mistakes and How to Avoid Them in the Square Root of 16/100

Students often make mistakes when finding the square root, such as forgetting to simplify fractions or using incorrect methods. Let's address some common mistakes.

Problem 1

If a square has an area of 16/100 square units, what is the side length of the square?

Okay, lets begin

The side length of the square is 0.2 units.

Explanation

The side length of a square is the square root of its area. √(16/100) = 0.2 Thus, the side length is 0.2 units.

Well explained 👍

Problem 2

A rectangular field has an area of 16/100 square meters. If the width is 0.4 meters, what is the length?

Okay, lets begin

The length is 0.4 meters.

Explanation

Area = length × width

16/100 = length × 0.4 Length = (16/100) ÷ 0.4 = 0.4 meters

Well explained 👍

Problem 3

Calculate √(16/100) × 5.

Okay, lets begin

The result is 1.0.

Explanation

First, find the square root of 16/100, which is 0.2. Then, multiply 0.2 by 5: 0.2 × 5 = 1.0

Well explained 👍

Problem 4

What is the square root of (4/10)²?

Okay, lets begin

The square root is 4/10 or 0.4.

Explanation

(4/10)² = 16/100 √(16/100) = 4/10 = 0.4

Well explained 👍

Problem 5

If the side of a square is √(16/100) meters, what is the perimeter of the square?

Okay, lets begin

The perimeter is 0.8 meters.

Explanation

Perimeter of a square = 4 × side length Side length = √(16/100) = 0.2 Perimeter = 4 × 0.2 = 0.8 meters

Well explained 👍

FAQ on Square Root of 16/100

1.What is √(16/100) in its simplest form?

The simplest form of √(16/100) is 0.2, as the fraction simplifies to (4/10).

2.What are the factors of 16 and 100?

Factors of 16 are 1, 2, 4, 8, and 16. Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

3.Calculate the square of 16/100.

The square of 16/100 is (16/100)² = 0.16² = 0.0256.

4.Is 16/100 a perfect square?

Yes, 16/100 is a perfect square, as it can be expressed as (4/10)².

5.Is 16/100 a rational number?

Yes, 16/100 is a rational number because it can be expressed as a fraction of integers.

Important Glossaries for the Square Root of 16/100

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4.
  • Rational number: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 16 is a perfect square because 4 × 4 = 16.
  • Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator and a denominator.
  • Decimal: A decimal is a way of representing numbers that have a whole part and a fractional part, separated by a decimal point. Example: 0.2 is a decimal.

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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.