130 LearnersLast updated on May 26th, 2025
Square Root of 6300
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 6300.
What is the Square Root of 6300?
The square root is the inverse of the square of the number. 6300 is not a perfect square. The square root of 6300 is expressed in both radical and exponential form. In the radical form, it is expressed as √6300, whereas (6300)^(1/2) in the exponential form. √6300 ≈ 79.37, 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 6300
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 6300 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6300 is broken down into its prime factors.
Step 1: Finding the prime factors of 6300 Breaking it down, we get 2 x 2 x 3 x 3 x 5 x 5 x 7: 2^2 x 3^2 x 5^2 x 7
Step 2: Now we found the prime factors of 6300. The second step is to make pairs of those prime factors. Since 6300 is not a perfect square, therefore the digits of the number can’t be grouped in pairs completely.
Therefore, calculating 6300 using prime factorization alone is not feasible.
Square Root of 6300 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. In the case of 6300, we need to group it as 63 and 00.
Step 2: Now we need to find n whose square is less than or equal to 63. We can say n is '7' because 7 x 7 = 49, which is less than 63. Now the quotient is 7 and the remainder is 63 - 49 = 14.
Step 3: Bring down the next pair, 00, making the new dividend 1400.
Step 4: Double the current quotient 7, giving us 14, which will be our new divisor's prefix.
Step 5: Determine a new digit for the divisor, such that 14x x x is less than or equal to 1400. Trying 9, we get 149 x 9 = 1341.
Step 6: Subtract 1341 from 1400, the difference is 59, and the new quotient is 79.
Step 7: Since there are no more digits to bring down, add a decimal point and continue with zero pairs.
Step 8: Bring down 00, making the new dividend 5900.
Step 9: The new divisor is 158, and we try 3, as 1583 x 3 = 4749.
Step 10: Subtracting 4749 from 5900 gives us 1151. The quotient now is 79.3.
Step 11: Continue this process until you reach the desired precision.
So the square root of √6300 is approximately 79.37.
Square Root of 6300 by Approximation Method
The approximation method is another method for 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 6300 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √6300.
The smallest perfect square less than 6300 is 6250 (which is 79^2) and the largest perfect square greater than 6300 is 6400 (which is 80^2). √6300 falls somewhere between 79 and 80.
Step 2: Now we need to apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (6300 - 6250) / (6400 - 6250) = 50 / 150 = 0.333. Adding this to 79 gives us 79 + 0.333 = 79.333. So, the square root of 6300 is approximately 79.37, rounding to two decimal places.
Common Mistakes and How to Avoid Them in the Square Root of 6300
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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 taking 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 the 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 before moving on to the second step.
For example: √(12+24) = √12 + √24 is the wrong method of using roots. 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 that 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. This may either happen in subtracting or elsewhere.
Square Root of 6300 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6300?
The area of the square is 6300 square units.
Explanation
The area of the square = side^2.
The side length is given as √6300.
Area of the square = side^2 = √6300 x √6300 = 6300.
Therefore, the area of the square box is 6300 square units.
Problem 2
A square-shaped building measuring 6300 square feet is built; if each of the sides is √6300, what will be the square feet of half of the building?
3150 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 6300 by 2, we get 3150.
So half of the building measures 3150 square feet.
Problem 3
Calculate √6300 x 5.
Approximately 396.85
Explanation
The first step is to find the square root of 6300, which is approximately 79.37.
The second step is to multiply 79.37 by 5.
So 79.37 x 5 ≈ 396.85.
Problem 4
What will be the square root of (6250 + 50)?
The square root is 80.
Explanation
To find the square root, we need to find the sum of (6250 + 50). 6250 + 50 = 6300, and then √6300 ≈ 79.37.
Therefore, the approximate square root of (6250 + 50) is ±79.37.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √6300 units and the width 'w' is 38 units.
We find the perimeter of the rectangle as approximately 234.74 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√6300 + 38) ≈ 2 × (79.37 + 38) ≈ 2 × 117.37 ≈ 234.74 units.
FAQ on Square Root of 6300
1.What is √6300 in its simplest form?
2.Mention the factors of 6300.
3.Calculate the square of 6300.
4.Is 6300 a prime number?
5.6300 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 6300?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 6300?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 6300
- Square root: A square root is the inverse of a square. For example, 4^2 = 16 and the inverse of the square is the square root, which 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. This is why it is also known as the principal square root.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Long division method: A method used to find the square root of non-perfect squares through a series of division steps.
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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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