Square Root of 81/100
2026-02-28 06:07 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-81/100

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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. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 81/100.

What is the Square Root of 81/100?

The square root is the inverse of the square of the number. 81/100 is a perfect square. The square root of 81/100 is expressed in both radical and exponential form. In the radical form, it is expressed as √(81/100), whereas (81/100)^(1/2) in the exponential form. √(81/100) = 9/10, 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 81/100

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, methods like the long-division method and approximation method are used. However, since 81/100 is a perfect square, let's explore the prime factorization method:

  • Prime factorization method
  • Long Division method
  • Approximation method

Square Root of 81/100 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 81/100 is broken down into its prime factors.

Step 1: Finding the prime factors of 81 and 100 Breaking them down, we get 81 = 3 x 3 x 3 x 3 = 3^4 and 100 = 2 x 2 x 5 x 5 = 2^2 x 5^2

Step 2: Now we found out the prime factors of 81 and 100. Since both are perfect squares, we can take the square root of each separately. √(81/100) = √81 / √100 = 9/10

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Square Root of 81/100 by Long Division Method

The long division method is generally used for non-perfect square numbers. However, for completeness, let's outline it here for 81/100.

Step 1: Since 81/100 is a fraction, find the square root of the numerator and the denominator separately.

Step 2: The square root of 81 is 9 and the square root of 100 is 10.

Step 3: Therefore, the square root of 81/100 is 9/10.

Square Root of 81/100 by Approximation Method

The approximation method is not needed for perfect squares, but we can briefly describe it here.

Step 1: Since 81/100 is a known perfect square, this method is not required. However, if it were not a perfect square, we would estimate between the nearest perfect squares.

Step 2: For 81/100, since it is a perfect square, the square root is exactly 9/10.

Common Mistakes and How to Avoid Them in the Square Root of 81/100

Students sometimes make mistakes while finding square roots, such as forgetting about the properties of fractions. Let's look at a few common mistakes.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(81/100)?

Okay, lets begin

The area of the square is 0.81 square units.

Explanation

The area of the square = side^2.

The side length is given as √(81/100).

Area of the square = (√(81/100))^2 = (9/10) × (9/10) = 0.81

Therefore, the area of the square box is 0.81 square units.

Well explained 👍

Problem 2

A square-shaped plot measures 81/100 square meters; if each of the sides is √(81/100), what will be the square meters of half of the plot?

Okay, lets begin

0.405 square meters

Explanation

We can just divide the given area by 2 as the plot is square-shaped.

Dividing 0.81 by 2 = we get 0.405.

So half of the plot measures 0.405 square meters.

Well explained 👍

Problem 3

Calculate √(81/100) × 5.

Okay, lets begin

4.5

Explanation

The first step is to find the square root of 81/100, which is 9/10.

The second step is to multiply 9/10 with 5.

So (9/10) × 5 = 4.5.

Well explained 👍

Problem 4

What will be the square root of (81 + 19)?

Okay, lets begin

The square root is 10.

Explanation

To find the square root, we need to find the sum of (81 + 19). 81 + 19 = 100, and then √100 = 10.

Therefore, the square root of (81 + 19) is ±10.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(81/100) units and the width ‘w’ is 1 unit.

Okay, lets begin

We find the perimeter of the rectangle as 2.8 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√(81/100) + 1) = 2 × (0.9 + 1) = 2 × 1.9 = 3.8 units.

Well explained 👍

FAQ on Square Root of 81/100

1.What is √(81/100) in its simplest form?

The prime factorization of 81 is 3^4 and of 100 is 2^2 × 5^2, so the simplest form of √(81/100) = 9/10.

2.Mention the factors of 81 and 100.

Factors of 81 are 1, 3, 9, 27, and 81. Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

3.Calculate the square of 81/100.

We get the square of 81/100 by multiplying the number by itself, that is (81/100) × (81/100) = 6561/10000 = 0.6561.

4.Is 81/100 a rational number?

Yes, 81/100 is a rational number because it can be expressed as the fraction of two integers.

5.What are the multiples of 81/100?

Multiples of 81/100 include numbers like 81/100, 162/100, 243/100, 324/100, etc., which are obtained by multiplying 81/100 by integers.

Important Glossaries for the Square Root of 81/100

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root that is √16 = 4.
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
  • Perfect square: A perfect square is a number that has an integer as its square root. For example, 81 is a perfect square because its square root is 9.
  • Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It is expressed as a/b, where a is the numerator and b is the denominator.
  • Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, for example, 0.9, 1.5, and 2.75 are decimals.

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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.