122 LearnersLast updated on May 26th, 2025
Square Root of 6272
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, including vehicle design, finance, etc. Here, we will discuss the square root of 6272.
What is the Square Root of 6272?
The square root is the inverse of the square of the number. 6272 is not a perfect square. The square root of 6272 is expressed in both radical and exponential form. In radical form, it is expressed as √6272, whereas (6272)^(1/2) in exponential form. √6272 ≈ 79.204, 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 6272
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not typically used for non-perfect square numbers, where long division and approximation methods are preferred. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 6272 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6272 is broken down into its prime factors:
Step 1: Finding the prime factors of 6272 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7: 2^6 x 7^2
Step 2: Now we have found the prime factors of 6272. The second step is to make pairs of those prime factors. Since 6272 is not a perfect square, therefore the digits of the number can’t be grouped completely into pairs for a perfect square. Calculating 6272 using prime factorization gives us a simplified radical form: 2^3 x 7 = 56√2
Square Root of 6272 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we calculate the square root by iterative division. Let us now learn how to find the square root using the long division method, step by step:
Step 1: To begin with, we need to group the numbers from right to left. In the case of 6272, we need to group it as 62 and 72.
Step 2: Determine the largest number whose square is less than or equal to 62. This number is 7, because 7 x 7 = 49. Subtract 49 from 62 to get a remainder of 13.
Step 3: Bring down the next pair of digits, which is 72, making the new dividend 1372.
Step 4: Double the quotient (7) to get 14 and determine the next digit of the quotient, which, when appended to 14 and multiplied by the same digit, gives a product less than or equal to 1372. This digit is 9, because 149 x 9 = 1341.
Step 5: Subtract 1341 from 1372 to get a remainder of 31.
Step 6: Add a decimal point to the quotient and bring down pairs of zeroes to continue. Continue these steps until you reach the desired decimal precision.
The value of √6272 is approximately 79.204.
Square Root of 6272 by Approximation Method
The approximation method is another approach to finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 6272 using the approximation method:
Step 1: Identify the closest perfect squares around 6272.
The closest perfect square less than 6272 is 6084 (which is 78^2), and the closest perfect square greater than 6272 is 6400 (which is 80^2). Thus, √6272 falls between 78 and 80.
Step 2: Apply linear approximation: (6272 - 6084) / (6400 - 6084) = 188 / 316 ≈ 0.595 Using this, add the result to the square root of the smaller perfect square: √6272 ≈ 78 + 0.595 = 78.595
This approximation can be further refined to achieve more precision if needed.
Common Mistakes and How to Avoid Them in the Square Root of 6272
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's look at 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, we typically use the positive square root in practical applications.
For example, √50 = ±7.071, but we often use only the positive value.
Mistake 2
Not adding the square root symbol in proper places
Proper use of the square root symbol is crucial. Simplifying expressions within the square root is important before proceeding.
For example, √(12 + 24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
To find the square root of a non-perfect square, breaking down the number correctly is important to avoid errors in approximation.
For example, approximating √50 as 7 is incorrect; the correct value is approximately 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students should understand the difference between square roots and cube roots.
For example, √50 and ∛50 are different operations and yield different results.
Mistake 5
Making mistakes in long division
The Long Division method involves multiple steps, leading to potential mistakes if steps are skipped or calculations are incorrect. Careful attention is needed, especially in subtraction and bringing down numbers.
Square Root of 6272 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6272?
The area of the square is 6272 square units.
Explanation
The area of the square = side^2.
Given the side length is √6272, the area is: Area = (√6272)^2 = 6272.
Therefore, the area of the square box is 6272 square units.
Problem 2
A square-shaped building measures 6272 square feet. If each of the sides is √6272, what will be the square feet of half of the building?
3136 square feet
Explanation
To find half of the area of the building, divide the total area by 2: Total area = 6272 square feet Half the area = 6272 ÷ 2 = 3136 square feet So half of the building measures 3136 square feet.
Problem 3
Calculate √6272 x 5.
396.02
Explanation
First, find the square root of 6272, which is approximately 79.204.
Then multiply by 5: 79.204 x 5 = 396.02
Problem 4
What will be the square root of (6272 + 28)?
The square root is approximately 80.
Explanation
To find the square root, first calculate the sum: 6272 + 28 = 6300
The square root of 6300 is approximately 79.37, which rounds to approximately 80.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √6272 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 258.41 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√6272 + 50) = 2 × (79.204 + 50) = 2 × 129.204 = 258.41 units.
FAQ on Square Root of 6272
1.What is √6272 in its simplest form?
2.Mention the factors of 6272.
3.Calculate the square of 6272.
4.Is 6272 a prime number?
5.6272 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 6272?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 6272?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 6272
- Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the square root of 16 is √16 = 4.
- Irrational number: An irrational number is one that cannot be written in the form of p/q, where p and q are integers and q is not equal to zero.
- Principal square root: This is the non-negative square root of a number, representing the positive solution.
- Prime factorization: The expression of a number as a product of its prime factors.
- Approximation: Estimating a number close to its exact value, often used for square roots of non-perfect squares.
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Jaskaran Singh Saluja
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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.
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