101 LearnersLast updated on May 26th, 2025
Square Root of 7.6
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 7.6.
What is the Square Root of 7.6?
The square root is the inverse of the square of the number. 7.6 is not a perfect square. The square root of 7.6 is expressed in both radical and exponential form. In the radical form, it is expressed as √7.6, whereas (7.6)^(1/2) in the exponential form. √7.6 ≈ 2.75681, 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 7.6
The prime factorization method is 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:
- Long division method
- Approximation method
Square Root of 7.6 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check 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, treat the number as 7.60, and group the numbers from right to left.
Step 2: Find a number whose square is less than or equal to 7. Here, 2 satisfies this condition because 2 × 2 = 4.
Step 3: Subtract 4 from 7, giving a remainder of 3. Bring down 60 to make it 360.
Step 4: Double the quotient obtained (2) to form part of the new divisor, making it 4_.
Step 5: Find a digit to fill in the blank that, when multiplied by the new divisor, does not exceed 360. Here, 7 works since 47 × 7 = 329.
Step 6: Subtract 329 from 360, giving a remainder of 31.
Step 7: Since we are not done, add a decimal point and bring down two zeros, making it 3100.
Step 8: Continue this process to refine the answer to two decimal places. The quotient will approximate to 2.75.
Square Root of 7.6 by Approximation Method
The approximation method is another technique for finding square roots. This is an easy method to find the square root of a given number. Let us learn how to find the square root of 7.6 using the approximation method.
Step 1: Identify the closest perfect squares around 7.6.
The closest perfect square less than 7.6 is 4, and the closest perfect square greater than 7.6 is 9. √7.6 falls between 2 and 3.
Step 2: Use interpolation: (Given number - smaller perfect square) / (greater perfect square - smaller perfect square) = (7.6 - 4) / (9 - 4) = 0.72
Step 3: Add this result to the smaller perfect square's root: 2 + 0.72 = 2.72
Thus, the approximate square root of 7.6 is about 2.72.
Common Mistakes and How to Avoid Them in the Square Root of 7.6
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Here are a few common mistakes students may make.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, the principal square root is usually the positive one, which is typically used in practical applications.
For example: √50 = 7.07, but there is also -7.07, which should not be overlooked.
Square Root of 7.6 Examples
Problem 1
Can you help Max find the area of a square if its side length is given as √7.6?
The area of the square is 7.6 square units.
Explanation
The area of a square = side².
The side length is given as √7.6.
Area of the square = side² = √7.6 × √7.6 = 7.6.
Therefore, the area is 7.6 square units.
Problem 2
A square-shaped park measures 7.6 square meters in area. If each side is √7.6, what will be the area of half of the park?
3.8 square meters
Explanation
To find half the area of the park, divide the total area by 2. 7.6 / 2 = 3.8.
Thus, half the park measures 3.8 square meters.
Problem 3
Calculate √7.6 × 3.
8.27043
Explanation
First, find the square root of 7.6, which is approximately 2.75681.
Then multiply 2.75681 by 3. 2.75681 × 3 ≈ 8.27043.
Problem 4
What will be the square root of (3.6 + 4)?
The square root is 2.8.
Explanation
To find the square root, first find the sum of (3.6 + 4). 3.6 + 4 = 7.6. √7.6 ≈ 2.8.
Therefore, the square root of (3.6 + 4) is ±2.8.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √7.6 units and the width 'w' is 5 units.
The perimeter of the rectangle is approximately 15.51 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√7.6 + 5) ≈ 2 × (2.75681 + 5) ≈ 15.51 units.
FAQ on Square Root of 7.6
1.What is √7.6 in its simplest form?
2.Is 7.6 a perfect square?
3.Calculate the square of 7.6.
4.Is 7.6 a prime number?
5.Is the square root of 7.6 rational or irrational?
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 7.6?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 7.6?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 7.6
- 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.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Decimal: A decimal is a number that has a whole number and a fractional part, such as 7.86, 8.65, and 9.42.
- Approximation: Calculating a value that is close to but not exactly the true value, often used for irrational numbers like square roots.
- Long division method: A technique used to find the square root of non-perfect squares by dividing the number into pairs and calculating step by step.
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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.
