142 LearnersLast updated on May 26th, 2025
Square Root of 84.64
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 84.64.
What is the Square Root of 84.64?
The square root is the inverse of squaring a number. 84.64 is not a perfect square. The square root of 84.64 can be expressed in both radical and exponential forms.
In radical form, it is expressed as √84.64, whereas in exponential form it is expressed as (84.64)(1/2). √84.64 = 9.2, 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 84.64
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers, methods such as the long division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 84.64 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we find the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left, taking two digits at a time. For 84.64, we consider 84 and 64.
Step 2: Find a number whose square is closest to or less than 84. It's 9, because 9 × 9 = 81, which is less than 84. The quotient is 9, and the remainder is 84 - 81 = 3.
Step 3: Bring down the next pair, 64, to make it 364.
Step 4: Double the quotient (which is 9) to get 18, and consider 18_ as the new divisor.
Step 5: Find a digit to place in the blank so that (18_ × _) is less than or equal to 364. The digit is 2 because 182 × 2 = 364.
Step 6: Subtract 364 from 364 to get 0. Since the remainder is 0, the square root of 84.64 is 9.2.
Square Root of 84.64 by Approximation Method
The approximation method is a simpler method for finding square roots. Let us learn how to find the square root of 84.64 using the approximation method.
Step 1: Identify perfect squares around 84.64. The closest perfect squares are 81 (which is 92) and 100 (which is 102). √84.64 is between 9 and 10.
Step 2: Using a more precise approximation, we find that 9.2 is very close to √84.64 since 9.2 × 9.2 = 84.64.
Common Mistakes and How to Avoid Them in the Square Root of 84.64
Students often make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in methods like long division. Here are a few common mistakes and how to avoid them.
Mistake 1
Forgetting about the negative square root
It's important to remember that a number has both positive and negative square roots. However, we usually focus on the positive square root, as it is more commonly used.
For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Square root of 84.64 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √84.64?
The area of the square is 84.64 square units.
Explanation
The area of a square is given by side2.
The side length is given as √84.64.
Area of the square = side2 = √84.64 × √84.64 = 9.2 × 9.2 = 84.64
Therefore, the area of the square box is 84.64 square units.
Problem 2
A square-shaped building measuring 84.64 square feet is built; if each of the sides is √84.64, what will be the square feet of half of the building?
42.32 square feet
Explanation
We can divide the given area by 2 since the building is square-shaped.
Dividing 84.64 by 2, we get 42.32.
So, half of the building measures 42.32 square feet.
Problem 3
Calculate √84.64 × 3.
27.6
Explanation
First, find the square root of 84.64, which is 9.2.
Then multiply 9.2 by 3. So, 9.2 × 3 = 27.6.
Problem 4
What will be the square root of (84.64 + 15.36)?
The square root is 10.
Explanation
First, find the sum of (84.64 + 15.36). 84.64 + 15.36 = 100, and then √100 = 10.
Therefore, the square root of (84.64 + 15.36) is ±10.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √84.64 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is 58.4 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√84.64 + 20)
= 2 × (9.2 + 20)
= 2 × 29.2
= 58.4 units.
FAQ on Square Root of 84.64
1.What is √84.64 in its simplest form?
2.Is 84.64 a perfect square?
3.Calculate the square of 84.64.
4.Is 84.64 a rational number?
5.Is the square root of 84.64 an integer?
Important Glossaries for the Square Root of 84.64
- 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 can be expressed as a fraction where the numerator and the denominator are integers, and the denominator is not zero.
- Perfect square: A perfect square is a number that has an integer as its square root. Example: 81 is a perfect square because √81 = 9.
- Long division method: A step-by-step method used to find the square root of a number, especially when dealing with non-perfect squares.
- Approximation method: A technique used to estimate the square root of a number by comparing it to nearby perfect squares.
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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.
