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444 LearnersLast updated on August 5, 2025
Square Root of 6.76
What is the Square Root of 6.76?
The square root is the inverse of the square of the number. 6.76 is a perfect square. The square root of 6.76 is expressed in both radical and exponential form. In radical form, it is expressed as √6.76, whereas (6.76)^(1/2) in exponential form. √6.76 = 2.6, 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 6.76
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, other methods like long-division and approximation are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
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Square Root of 6.76 by Long Division Method
The long division method is particularly used for non-perfect square numbers but can also be applied for precision. However, since 6.76 is already a perfect square, we know its square root is 2.6.
Square Root of 6.76 by Approximation Method
The approximation method is another method for finding square roots and is useful for non-perfect squares. However, since 6.76 is a perfect square, we directly know that √6.76 = 2.6.
Common Mistakes and How to Avoid Them in the Square Root of 6.76
Students do make mistakes while finding the square root, such as forgetting about the negative square root. Skipping long division methods etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we typically take only the positive square root, as it is the required one.
For example, √6.76 = 2.6, but there is also -2.6, which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root symbol properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on to the next step.
For example, √(4 + 5) ≠ √4 + √5. The correct usage is √(4 + 5) = √9 = 3.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For Example, √7 ≈ 2.64575, not 3.
Mistake 5
Making mistakes in long division
Finding a square root using the Long Division method involves many steps. Due to this, many students might skip a step accidentally, resulting in a wrong answer at the end of the sum. This may happen during subtraction or elsewhere.
Square root of 6.76 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √7?
The area of the square is approximately 49 square units.
Explanation
The area of the square = side^2.
The side length is given as √7.
Area of the square = side^2 = √7 × √7 ≈ 2.64575 × 2.64575 ≈ 7.
Therefore, the area of the square box is approximately 7 square units.
Problem 2
A square-shaped building measuring 6.76 square feet is built; if each of the sides is √6.76, what will be the square feet of half of the building?
3.38 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 6.76 by 2 = we get 3.38.
So half of the building measures 3.38 square feet.
Problem 3
Calculate √6.76 × 5.
13
Explanation
The first step is to find the square root of 6.76, which is 2.6.
The second step is to multiply 2.6 by 5. So, 2.6 × 5 = 13.
Problem 4
What will be the square root of (4 + 2.76)?
The square root is 2.6.
Explanation
To find the square root, we need to find the sum of (4 + 2.76). 4 + 2.76 = 6.76, and then √6.76 = 2.6.
Therefore, the square root of (4 + 2.76) is ±2.6.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √6.76 units and the width ‘w’ is 8 units.
The perimeter of the rectangle is 21.2 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√6.76 + 8) = 2 × (2.6 + 8) = 2 × 10.6 = 21.2 units.
FAQ on Square Root of 6.76
1.What is √6.76 in its simplest form?
2.Mention the factors of 6.76.
3.Calculate the square of 6.76.
4.Is 6.76 a prime number?
5.6.76 is divisible by?
Important Glossaries for the Square Root of 6.76
- Square root: A square root is the inverse of a square. Example: 5^2 = 25 and the inverse of the square is the square root, that is, √25 = 5.
- 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 number that is the square of an integer is called a perfect square. For example, 4, 9, and 16 are perfect squares.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal, for example, 7.86, 8.65, and 9.42 are decimals.
- Exponential form: A way to express numbers using a base and an exponent, indicating how many times the base is multiplied by itself. For example, 3^2 = 9.
Vikrant Sharma
About the Author
Vikrant is a passionate Mathematics teacher with over 5 years of teaching experience in both conventional and Vedic Maths. His student-focused approach combines clear concepts with motivation and encouragement, helping students build confidence and develo
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
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