Summarize this article:
634 LearnersLast updated on August 5, 2025
Square Root of 0.8
What is the Square Root of 0.8?
The square root is the inverse of the square of the number. 0.8 is not a perfect square. The square root of 0.8 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.8, whereas (0.8)^(1/2) in the exponential form. √0.8 ≈ 0.89443, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 0.8
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 0.8 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. For 0.8, we can express it as a fraction (8/10) or (4/5). Since 0.8 is not a perfect square, the prime factorization approach is not straightforward for decimal or fraction values without converting to a base that can be factored easily.
Hence, the prime factorization method is not typically used for decimals like 0.8.
Explore Our Programs
Square Root of 0.8 by Long Division Method
The long division method is particularly useful for non-perfect square numbers. Here's how to find the square root using the long division method, step by step:
Step 1: Begin by considering 0.8 as 80/100 or 0.80 for ease of calculation.
Step 2: Start with the closest perfect square less than 80, which is 64 (√64=8).
Step 3: Use the long division method to find √0.80, bringing down pairs of zeros as needed to find more decimal places.
Step 4: Continue the division process until you reach the desired precision.
Step 5: The result will be √0.8 ≈ 0.89443.
Square Root of 0.8 by Approximation Method
The approximation method is another method for finding square roots, useful for gaining a quick estimate. Here's how to find the square root of 0.8 using approximation:
Step 1: Identify perfect squares around 0.8. The closest perfect squares are 0.64 (0.8²) and 1 (1²), which are near 0.8.
Step 2: Recognize that √0.64 = 0.8 and √1 = 1, so √0.8 falls between 0.8 and 1.
Step 3: Use an average method or linear interpolation to find a closer approximation if necessary.
Step 4: The approximated value is √0.8 ≈ 0.89443.
Common Mistakes and How to Avoid Them in the Square Root of 0.8
Students often make mistakes while finding square roots, such as overlooking the negative square root or misapplying methods. Let's examine a few common errors in detail.
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 typically use only the positive square root in practical applications.
For example: √0.8 ≈ 0.89443, but there is also -0.89443.
Mistake 2
Not adding the square root symbol in proper places
Another common mistake is misusing the square root symbol. It's crucial to simplify the numbers inside the square root before proceeding.
For example: √(0.4 + 0.4) = √0.8 is correct, not √0.4 + √0.4.
Mistake 3
Not finding the correct value of a non-perfect square
It's crucial to simplify numbers inside the square root to avoid mistakes in identifying approximate values.
For example: √0.8 ≠ 0.9. The correct answer is √0.8 ≈ 0.89443.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Students might skip a step accidentally, leading to a wrong answer. This can occur in subtraction or elsewhere.
Square Root of 0.8 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.8?
The area of the square is approximately 0.8 square units.
Explanation
The area of a square = side².
The side length is given as √0.8.
Area of the square = (√0.8)² = 0.8.
Therefore, the area of the square box is approximately 0.8 square units.
Problem 2
A square-shaped garden measuring 0.8 square meters is built; if each of the sides is √0.8, what will be the square meters of half of the garden?
0.4 square meters
Explanation
Divide the given area by 2 as the garden is square-shaped.
Dividing 0.8 by 2, we get 0.4. So, half of the garden measures 0.4 square meters.
Problem 3
Calculate √0.8 × 5.
Approximately 4.47215
Explanation
The first step is to find the square root of 0.8, which is approximately 0.89443.
The second step is to multiply 0.89443 by 5. So, 0.89443 × 5 ≈ 4.47215.
Problem 4
What will be the square root of (0.6 + 0.2)?
The square root is approximately 0.89443.
Explanation
To find the square root, first find the sum of (0.6 + 0.2). 0.6 + 0.2 = 0.8, and then √0.8 ≈ 0.89443.
Therefore, the square root of (0.6 + 0.2) is approximately ±0.89443.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √0.8 units and the width ‘w’ is 0.5 units.
The perimeter of the rectangle is approximately 2.78886 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√0.8 + 0.5) = 2 × (0.89443 + 0.5) = 2 × 1.39443 ≈ 2.78886 units.
FAQ on Square Root of 0.8
1.What is √0.8 in its simplest form?
2.Can 0.8 be a perfect square?
3.Calculate the square of 0.8.
4.Is 0.8 a rational number?
5.What are the factors of 0.8?
Important Glossaries for the Square Root of 0.8
- Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse is √16 = 4.
- Irrational number: An irrational number cannot be written in the form of p/q, where p and q are integers, and q is not zero.
- Rational number: A number that can be expressed as a fraction p/q, where p and q are integers, and q is not zero.
- Decimal: A number with a whole number and a fractional part separated by a decimal point, such as 0.8.
- Approximation: Estimating a number to a certain degree of accuracy, often used for non-perfect squares or irrational numbers.
Vikrant Sharma
About the Author
Vikrant Sharma 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.
We use cookies for essential site function, analytics, and marketing. You can accept all, reject non-essential cookies, or customize your choices. See our Cookie Policy.