116 LearnersLast updated on May 26th, 2025
Square Root of 81/100
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
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.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically use the positive square root for real-world applications.
For example: √(81/100) = 9/10, but there is also -9/10.
Mistake 2
Not simplifying the fraction first
Not simplifying the fraction before taking the square root is a common mistake. Ensure fractions are in simplest form before proceeding.
For example: √(81/100) = 9/10.
Mistake 3
Confusing the square root of a fraction with the fraction of square roots
Students must recognize that √(a/b) = √a / √b, not (√a) / b or a / (√b).
For example: √(81/100) = √81 / √100.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root to avoid confusion.
For example: √81 and ∛81 are different.
Mistake 5
Misapplying the properties of square roots
Applying properties of square roots incorrectly can lead to mistakes. Be sure to understand that √(a*b) = √a * √b only when a and b are non-negative.
Square Root of 81/100 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(81/100)?
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.
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?
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.
Problem 3
Calculate √(81/100) × 5.
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.
Problem 4
What will be the square root of (81 + 19)?
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.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(81/100) units and the width ‘w’ is 1 unit.
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.
FAQ on Square Root of 81/100
1.What is √(81/100) in its simplest form?
2.Mention the factors of 81 and 100.
3.Calculate the square of 81/100.
4.Is 81/100 a rational number?
5.What are the multiples of 81/100?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 81/100?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 81/100?
9.Does learning Algebra support future career opportunities for students in Vietnam?
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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About BrightChamps in Vietnam
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
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