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127 LearnersLast updated on December 15, 2025
Square Root of 81/400
If a number is multiplied by the same number, 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 and finance. Here, we will discuss the square root of 81/400.
What is the Square Root of 81/400?
The square root is the inverse of the square of the number.
81/400 is a perfect square fraction.
The square root of 81/400 can be expressed in both radical and fractional form.
In radical form, it is expressed as √(81/400), whereas in fractional form, it is expressed as (81/400)^(1/2).
√(81/400) = 9/20, 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 81/400
The prime factorization method is used for perfect square numbers.
For perfect square fractions like 81/400, the square root can be determined by taking the square root of the numerator and the denominator separately.
Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 81/400 by Prime Factorization Method
The product of prime factors is the prime factorization of a number.
Now let us look at how 81 and 400 are broken down into their prime factors:
Step 1: Finding the prime factors of 81 and 400.
Breaking it down, we get 81 = 3 x 3 x 3 x 3 = 34, and 400 = 2 x 2 x 2 x 2 x 5 x 5 = 24 x 52.
Step 2: Now we find the square root by taking the square root of the prime factors.
√(81/400) = √81/√400 = 32/22 x 5 = 9/20.
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Square Root of 81/400 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also be used for fractions.
In this method, we should check the perfect square numbers for the given fraction.
Let us now learn how to find the square root using the long division method:
Step 1: Calculate the square roots of the numerator and the denominator separately using the long division method.
Step 2: The square root of 81 is 9 and the square root of 400 is 20.
Step 3: Combine the results to get the square root of the fraction: 9/20.
Square Root of 81/400 by Approximation Method
The approximation method is another method for finding square roots, but since 81/400 is a perfect square fraction, we can directly find its square root without approximation.
Step 1: Recognize that 81 is the square of 9 and 400 is the square of 20.
Step 2: Therefore, √(81/400) = 9/20.
Common Mistakes and How to Avoid Them in the Square Root of 81/400
Students do make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying the fraction.
Now let us look at a few of those mistakes that students tend to make in detail.
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 consider only the positive square root in practical applications.
For example: √(81/400) = 9/20, there is also -9/20 which should not be forgotten.
Mistake 2
Incorrectly simplifying fractions
Another mistake is not simplifying fractions correctly.
Ensure that each part of the fraction is reduced to its simplest form before applying the square root.
For example: √(81/400) = 9/20 is the simplest form.
Mistake 4
Misapplying the square root to non-perfect squares
While finding the square root of non-perfect squares, ensure that approximation methods or long division methods are applied correctly.
Mistake 5
Skipping steps in the prime factorization
When using prime factorization, ensure all steps are followed to simplify the square root correctly.
Skipping even a single step can lead to incorrect results.
Square Root of 81/400 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ(81/400)?
The area of the square is 0.2025 square units.
Explanation
The area of the square = side2.
The side length is given as √(81/400).
Area of the square = (9/20) x (9/20) = 0.2025.
Therefore, the area of the square box is 0.2025 square units.
Problem 2
A square-shaped garden measuring 81/400 square feet is built; if each of the sides is โ(81/400), what will be the square feet of half of the garden?
0.10125 square feet
Explanation
We can divide the given area by 2 as the garden is square-shaped.
Dividing 81/400 by 2 = 0.10125.
So half of the garden measures 0.10125 square feet.
Problem 3
Calculate โ(81/400) x 5.
2.25
Explanation
The first step is to find the square root of 81/400, which is 9/20.
The second step is to multiply 9/20 by 5.
So 9/20 x 5 = 2.25.
Problem 4
What will be the square root of (81/400 + 19/400)?
The square root is 1.
Explanation
To find the square root, we need to find the sum of (81/400 + 19/400). 81/400 + 19/400 = 100/400 = 1/4, and then √(1/4) = 1/2.
Therefore, the square root of (81/400 + 19/400) is ±1/2.
Problem 5
Find the perimeter of a rectangle if its length โlโ is โ(81/400) units and the width โwโ is 3/4 units.
We find the perimeter of the rectangle as 2.1 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (9/20 + 3/4) = 2 × (9/20 + 15/20) = 2 × (24/20) = 2 × 1.2 = 2.4 units.
FAQ on Square Root of 81/400
1.What is โ(81/400) in its simplest form?
2.Mention the factors of 81 and 400.
3.Calculate the square of 81/400.
4.Is 81/400 a prime fraction?
5.Is 81/400 a rational number?
Important Glossaries for the Square Root of 81/400
- Square root: A square root is the inverse of a square. Example: 42 = 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 is the square of an integer. For example, 81 is a perfect square because it is 92.
- Fraction: A fraction is a part of a whole expressed using a numerator and a denominator. For example, 81/400 is a fraction.
- Decimal: If a number has a whole number and a fraction in a single number then it is called a decimal. For example, 0.45, 0.75, and 0.95 are decimals.
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.
