103 LearnersLast updated on May 26th, 2025
Square Root of 0.75
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 various fields such as geometry, engineering, and finance. Here, we will discuss the square root of 0.75.
What is the Square Root of 0.75?
The square root is the inverse of the square of a number. 0.75 is not a perfect square. The square root of 0.75 can be expressed in both radical and exponential forms. In radical form, it is expressed as √0.75, whereas in exponential form, it is expressed as (0.75)^(1/2). √0.75 ≈ 0.86603, which is an irrational number because it cannot be expressed as a simple fraction of two integers.
Finding the Square Root of 0.75
For non-perfect square numbers like 0.75, methods such as the long division method and approximation method are often used. Let us now learn these methods:
- Long division method
- Approximation method
Square Root of 0.75 by Long Division Method
The long division method is particularly useful for finding the square root of non-perfect square numbers. Here is how to find the square root of 0.75 using this method:
Step 1: Start by placing a bar over 75 (considering it as 0.75 by ignoring the decimal for now).
Step 2: Find a number whose square is less than or equal to 75. In this case, 8 * 8 = 64 is less than 75.
Step 3: Subtract 64 from 75, getting a remainder of 11. Bring down 00 to make it 1100.
Step 4: Double the divisor (8), getting 16. Find a number that, when placed next to 16, results in a product less than or equal to 1100. This number is 6, as 166 * 6 = 996.
Step 5: Subtract 996 from 1100, leaving a remainder of 104. Bring down 00 to make it 10400.
Step 6: Continue the process until you reach the desired number of decimal places.
The quotient obtained is approximately 0.86603.
Square Root of 0.75 by Approximation Method
The approximation method is another way to find square roots, especially for non-perfect squares. Here is how to approximate the square root of 0.75:
Step 1: Identify two perfect squares between which 0.75 lies. It lies between √0.64 (which is 0.8) and √1 (which is 1).
Step 2: Use the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). For 0.75, the formula is (0.75 - 0.64) / (1 - 0.64) = 0.11 / 0.36 = 0.3056.
Step 3: Add the result to the square root of the smaller perfect square: 0.8 + 0.3056 = 1.1056. This is not accurate due to a mistake in the approximation; instead, the closer approximation is √0.75 ≈ 0.86603.
Common Mistakes and How to Avoid Them in the Square Root of 0.75
Students often make mistakes while calculating square roots, such as forgetting about the negative square root or mishandling decimal points. Here are a few common mistakes and how to avoid them.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, in many practical applications, we consider only the positive square root.
For example, √0.75 ≈ 0.86603, but there is also -0.86603.
Square Root of 0.75 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.75?
The area of the square is approximately 0.5625 square units.
Explanation
The area of a square = side^2.
The side length is given as √0.75.
Area = (√0.75) × (√0.75) = 0.75.
Therefore, the area of the square box is approximately 0.5625 square units.
Problem 2
A square-shaped garden measures 0.75 square meters. If each side measures √0.75, what will be half the area of the garden?
0.375 square meters
Explanation
Since the area of the garden is 0.75 square meters, half of it is simply 0.75 / 2 = 0.375 square meters.
Problem 3
Calculate √0.75 × 5.
Approximately 4.33015
Explanation
First, find the square root of 0.75, which is approximately 0.86603.
Then, multiply it by 5. 0.86603 × 5 = 4.33015.
Problem 4
What will be the square root of (0.64 + 0.11)?
The square root is approximately 0.86603.
Explanation
First, find the sum of 0.64 + 0.11 = 0.75.
Then, find the square root of 0.75, which is approximately 0.86603.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √0.75 units and the width 'w' is 0.5 units.
The perimeter of the rectangle is approximately 2.73206 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√0.75 + 0.5) = 2 × (0.86603 + 0.5) = 2 × 1.36603 = 2.73206 units.
FAQ on Square Root of 0.75
1.What is √0.75 in its simplest form?
2.What are the factors of 0.75?
3.Calculate the square of 0.75.
4.Is 0.75 a prime number?
5.0.75 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 0.75?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 0.75?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 0.75
- Square root: A square root is the inverse operation of squaring a number. For example, the square root of 9 is 3, as 3^2 = 9.
- Irrational number: An irrational number cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating.
- Decimal: A decimal is a fraction written in a special form. Instead of a numerator and denominator, a decimal uses a decimal point. Examples include 0.5, 0.75, and 0.86603.
- Approximation: Finding a value that is close to the actual answer. For example, the square root of 0.75 is approximately 0.86603.
- Long division method: A step-by-step approach for dividing numbers to find the square root of non-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
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