120 LearnersLast updated on May 26th, 2025
Square Root of 6200
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 6200.
What is the Square Root of 6200?
The square root is the inverse of the square of the number. 6200 is not a perfect square. The square root of 6200 is expressed in both radical and exponential form. In the radical form, it is expressed as √6200, whereas (6200)^(1/2) in the exponential form. √6200 ≈ 78.7401, 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 6200
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 6200 by Prime Factorization Method
The product of prime factors is the Prime factorization of a number. Now let us look at how 6200 is broken down into its prime factors.
Step 1: Finding the prime factors of 6200 Breaking it down, we get 2 x 2 x 2 x 5 x 5 x 31: 2^3 x 5^2 x 31
Step 2: Now we found the prime factors of 6200. The second step is to make pairs of those prime factors. Since 6200 is not a perfect square, the digits of the number can’t be grouped in pairs perfectly.
Therefore, calculating 6200 using prime factorization directly to get a whole number is impossible.
Square Root of 6200 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, we need to group the numbers from right to left. For 6200, we would group it as 62 and 00.
Step 2: Now we need to find n whose square is ≤ 62. We can say n as ‘7’ because 7 x 7 = 49 is less than 62. Now the quotient is 7 after subtracting 49 from 62, the remainder is 13.
Step 3: Bring down the next pair of digits, which is 00, making the new dividend 1300. Add the last divisor to the same number (7 + 7) to get 14, which will be our new divisor.
Step 4: Now, find the largest digit n such that 14n x n ≤ 1300. Let n = 9, then 149 x 9 = 1341, which is too large. Try n = 8, 148 x 8 = 1184, which is fine.
Step 5: Subtract 1184 from 1300, the difference is 116. The quotient now is 78.
Step 6: Since the dividend is less than the divisor, we add a decimal point and bring down two zeros making the dividend 11600.
Step 7: Find the new divisor. It is 156, because 1560 x 7 = 10920.
Step 8: Subtract 10920 from 11600, the result is 680.
Step 9: The quotient is 78.7. Repeat the process to find more decimal places if needed.
So the square root of √6200 is approximately 78.74.
Square Root of 6200 by Approximation Method
The approximation method is another method for finding the 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 6200 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √6200.
The smallest perfect square less than 6200 is 6084 (78^2), and the largest perfect square greater than 6200 is 6241 (79^2). √6200 falls somewhere between 78 and 79.
Step 2: Now we need to apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Applying the formula, (6200 - 6084) / (6241 - 6084) = 116 / 157 ≈ 0.739.
Using the formula, we identified the decimal point of our square root. The next step is adding the integer part we got initially to the decimal number, which is 78 + 0.739 = 78.739, so the square root of 6200 is approximately 78.739.
Common Mistakes and How to Avoid Them in the Square Root of 6200
Students do make mistakes while finding the square root, like 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 will be considering only the positive square root, as it is the required one.
For example: √50 = 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12 + 24) = √12 + √24 is wrong. The right way of using roots is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example: √50 and ∛50 are different.
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, which results in a wrong answer at the end of the calculation. This may either happen in subtracting or elsewhere.
Square Root of 6200 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6200?
The area of the square is approximately 6200 square units.
Explanation
The area of the square = side^2.
The side length is given as √6200.
Area of the square = (√6200) x (√6200) = 6200 square units.
Therefore, the area of the square box is approximately 6200 square units.
Problem 2
A square-shaped building measuring 6200 square feet is built; if each of the sides is √6200, what will be the square feet of half of the building?
3100 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 6200 by 2 = 3100
So half of the building measures 3100 square feet.
Problem 3
Calculate √6200 x 5.
Approximately 393.7
Explanation
The first step is to find the square root of 6200, which is approximately 78.74.
The second step is to multiply 78.74 with 5.
So 78.74 x 5 ≈ 393.7
Problem 4
What will be the square root of (6000 + 200)?
The square root is approximately 78.74.
Explanation
To find the square root, we need to find the sum of (6000 + 200). 6000 + 200 = 6200, and then the square root of 6200 ≈ 78.74.
Therefore, the square root of (6000 + 200) is approximately ±78.74.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √6200 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 257.48 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√6200 + 50) = 2 × (78.74 + 50) = 2 × 128.74 = 257.48 units.
FAQ on Square Root of 6200
1.What is √6200 in its simplest form?
2.Mention the factors of 6200.
3.Calculate the square of 6200.
4.Is 6200 a prime number?
5.6200 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 6200?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 6200?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 6200
- Square root: A square root is the inverse of a square. Example: 4^2 = 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.
- Perfect square: A number that is the square of an integer. Example: 144 is a perfect square because 12 x 12 = 144.
- Prime factorization: Expressing a number as the product of its prime factors. Example: The prime factorization of 60 is 2^2 x 3 x 5.
- Approximation: The process of finding a value that is close enough to the right answer, usually within a specified range.
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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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