152 LearnersLast updated on May 26th, 2025
Square Root of 6760
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 6760.
What is the Square Root of 6760?
The square root is the inverse of squaring a number. 6760 is not a perfect square. The square root of 6760 can be expressed in radical and exponential forms. In the radical form, it is expressed as √6760, whereas in exponential form, it is expressed as (6760)^(1/2). The approximate value of √6760 is 82.206, which is an irrational number because it cannot be expressed as a ratio of two integers.
Finding the Square Root of 6760
The prime factorization method is commonly used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are often employed. Let's explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 6760 by Prime Factorization Method
Prime factorization involves expressing a number as the product of its prime factors. Let's break down 6760 into its prime factors:
Step 1: Finding the prime factors of 6760 By breaking it down, we get 2 × 2 × 2 × 5 × 13 × 13: 2^3 × 5 × 13^2
Step 2: The prime factors of 6760 are identified. Since 6760 is not a perfect square, we cannot pair all the prime factors completely.
Therefore, calculating the exact square root using prime factorization is not straightforward.
Square Root of 6760 by Long Division Method
The long division method is suitable for finding the square root of non-perfect square numbers. Here is how to find the square root using the long division method, step by step:
Step 1: Begin by grouping the digits of 6760 from right to left. We can group them as 67 and 60.
Step 2: Find the largest number whose square is less than or equal to 67. In this case, 8² = 64. The quotient is 8, and the remainder is 67 - 64 = 3.
Step 3: Bring down the next pair of digits (60), making the new dividend 360. Double the quotient (8), resulting in a new divisor of 16_.
Step 4: Find a digit (n) such that 16n × n is less than or equal to 360. We find that n = 2 works because 162 × 2 = 324.
Step 5: Subtract 324 from 360 to get a remainder of 36, and the quotient becomes 82.
Step 6: Since the dividend is less than the divisor, add a decimal point to the quotient and bring down two zeros to make the new dividend 3600.
Step 7: Double the quotient part (82), resulting in a new divisor of 164_.
Step 8: Find the largest digit (n) such that 164n × n is less than or equal to 3600. We find that n = 2 works because 1642 × 2 = 3284.
Step 9: Subtract 3284 from 3600, resulting in a remainder of 316.
Step 10: Continue this process until an accurate square root value is reached.
The approximate square root of 6760 is 82.206.
Square Root of 6760 by Approximation Method
The approximation method is another way to find the square root of a number. Let's use it to find the square root of 6760:
Step 1: Identify the closest perfect squares around 6760. The perfect squares 6400 (80²) and 6889 (83²) bracket 6760. Therefore, √6760 is between 80 and 83.
Step 2: Use linear interpolation to approximate the square root: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (6760 - 6400) / (6889 - 6400) = 360 / 489 ≈ 0.736
Step 3: Add this decimal to the lower bound: 80 + 0.736 = 80.736. However, refining through further steps, we find the square root to be approximately 82.206.
Common Mistakes and How to Avoid Them in the Square Root of 6760
Students often make mistakes finding square roots, like forgetting negative roots or skipping steps. Here are some common errors and how to avoid them:
Mistake 1
Forgetting about the negative square root
Remind students that numbers have both positive and negative square roots. However, typically only the positive root is used in practical applications.
For example: √50 = 7.07, but remember there is also -7.07.
Mistake 2
Not adding the square root symbol in proper places
It's crucial to place the square root symbol correctly. Teach students that simplifying expressions inside the square root must be done before applying further operations.
For example: √(12 + 24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
Students should be taught to approximate non-perfect square roots accurately to avoid errors.
For example: √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Emphasize the difference between square roots and cube roots to prevent confusion.
For example, √50 and ∛50 are different operations.
Mistake 5
Making mistakes in long division
The long division method involves multiple steps. Skipping a step, such as incorrect subtraction, can lead to wrong answers. Practice careful step-by-step execution to avoid errors.
Square Root of 6760 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6760?
The area of the square is approximately 457,536.036 square units.
Explanation
The area of a square is calculated as side². The side length is given as √6760. Area = side² = (√6760)² = 6760 square units. Therefore, the area of the square box is approximately 457,536.036 square units.
Problem 2
A square-shaped garden measuring 6760 square feet is built. If each side is √6760, what is the square footage of half the garden?
3380 square feet
Explanation
Since the garden is square-shaped, you can divide the total area by 2 to find half the area. 6760 / 2 = 3380 So, half of the garden measures 3380 square feet.
Problem 3
Calculate √6760 x 5.
Approximately 411.03
Explanation
First, find the square root of 6760, which is approximately 82.206. Then, multiply by 5: 82.206 x 5 ≈ 411.03
Problem 4
What will be the square root of (6760 + 40)?
The square root is approximately 82.462
Explanation
First, find the sum: 6760 + 40 = 6800. Then, find the square root of 6800, which is approximately 82.462. Therefore, the square root of (6760 + 40) is approximately ±82.462.
Problem 5
Find the perimeter of a rectangle if its length is √6760 units and the width is 50 units.
The perimeter of the rectangle is approximately 264.412 units.
Explanation
Perimeter of a rectangle = 2 × (length + width) Perimeter = 2 × (√6760 + 50) Perimeter = 2 × (82.206 + 50) ≈ 2 × 132.206 = 264.412 units.
FAQ on Square Root of 6760
1.What is √6760 in its simplest form?
2.Mention the factors of 6760.
3.Calculate the square of 6760.
4.Is 6760 a prime number?
5.6760 is divisible by?
Important Glossaries for the Square Root of 6760
- Square root: The square root is the inverse of squaring a number. For example, 4² = 16, so √16 = 4.
- Irrational number: An irrational number cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 9 is a perfect square because it is 3².
- Long division method: A systematic method for finding the square root of non-perfect squares by dividing the number into groups of two digits.
- Interpolation: A method of estimating values between two known values. For example, finding √6760 by using perfect squares around it.
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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.
