104 LearnersLast updated on May 26th, 2025
Square Root of 0.64
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 0.64.
What is the Square Root of 0.64?
The square root is the inverse of the square of the number. 0.64 is a perfect square. The square root of 0.64 is expressed in both radical and exponential forms. In the radical form, it is expressed as √0.64, whereas (0.64)^(1/2) in the exponential form. √0.64 = 0.8, 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 0.64
For perfect square numbers like 0.64, we can use the prime factorization method. However, for non-perfect squares, methods like 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 0.64 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 0.64 is broken down into its prime factors.
Step 1: Finding the prime factors of 0.64 Breaking it down, we get 2^2 x (0.1)^2 = 0.64
Step 2: Now we found out the prime factors of 0.64. The second step is to make pairs of those prime factors. Since 0.64 is a perfect square, we can pair the factors.
Therefore, √0.64 = √(2^2 x (0.1)^2) = 0.8.
Square Root of 0.64 by Long Division Method
The long division method is particularly used for non-perfect square numbers. However, it can also verify perfect squares. 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. In the case of 0.64, we need to group it as 64.
Step 2: Now we need to find n whose square is closest to 64. We can say n as ‘8’ because 8 x 8 = 64. Now the quotient is 8 and the remainder is 0. Since the remainder is zero, the process stops here. So the square root of √0.64 is 0.8.
Square Root of 0.64 by Approximation Method
Approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 0.64 using the approximation method.
Step 1: Now we have to find the closest perfect square of √0.64. The perfect square closest to 0.64 is 0.64 itself. √0.64 falls exactly on 0.8.
Therefore, the square root of 0.64 is 0.8.
Common Mistakes and How to Avoid Them in the Square Root of 0.64
Students do make mistakes while finding the square root, like confusing decimal placement or incorrectly identifying square roots. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Misplacing the Decimal Point
When dealing with decimals, students often misplace the decimal point.
For instance, the square root of 0.64 is 0.8, not 8 or 0.08. Ensuring that the square root is correctly identified relative to the decimal place is crucial.
Square Root of 0.64 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.64?
The area of the square is 0.4096 square units.
Explanation
The area of the square = side^2.
The side length is given as √0.64.
Area of the square = side^2 = √0.64 x √0.64 = 0.8 × 0.8 = 0.64.
Therefore, the area of the square box is 0.64 square units.
Problem 2
A square-shaped building measuring 0.64 square meters is built; if each of the sides is √0.64, what will be the square meters of half of the building?
0.32 square meters
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 0.64 by 2 = we get 0.32.
So half of the building measures 0.32 square meters.
Problem 3
Calculate √0.64 x 5.
4.0
Explanation
The first step is to find the square root of 0.64, which is 0.8. The second step is to multiply 0.8 with 5. So, 0.8 x 5 = 4.0.
Problem 4
What will be the square root of (0.36 + 0.28)?
The square root is 0.8.
Explanation
To find the square root, we need to find the sum of (0.36 + 0.28). 0.36 + 0.28 = 0.64, and then √0.64 = 0.8.
Therefore, the square root of (0.36 + 0.28) is ±0.8.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √0.64 units and the width ‘w’ is 0.38 units.
We find the perimeter of the rectangle as 2.36 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√0.64 + 0.38) = 2 × (0.8 + 0.38) = 2 × 1.18 = 2.36 units.
FAQ on Square Root of 0.64
1.What is √0.64 in its simplest form?
2.What are the factors of 0.64?
3.Calculate the square of 0.64.
4.Is 0.64 a perfect square?
5.What is the square root of 0.64 as a fraction?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 0.64?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 0.64?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 0.64
- Square root: A square root is the inverse of a square. Example: 0.8^2 = 0.64 and the inverse of the square is the square root, that is √0.64 = 0.8.
- 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 or a rational number.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal, for example, 0.64, 1.25, and 3.14 are decimals.
- Exponential form: Expressing a number as a power, for example, (0.64)^(1/2) represents the square root of 0.64.
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About BrightChamps in Qatar
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.
