122 LearnersLast updated on May 26th, 2025
Square Root of 6075
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 6075.
What is the Square Root of 6075?
The square root is the inverse of the square of a number. 6075 is not a perfect square. The square root of 6075 is expressed in both radical and exponential form. In the radical form, it is expressed as √6075, whereas in exponential form as (6075)^(1/2). √6075 ≈ 78, 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 6075
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like 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 6075 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6075 is broken down into its prime factors.
Step 1: Finding the prime factors of 6075 Breaking it down, we get 3 x 3 x 3 x 5 x 5 x 3 x 3: (3^5) x (5^2)
Step 2: Now we found out the prime factors of 6075. The second step is to make pairs of those prime factors. Since 6075 is not a perfect square, complete pairs cannot be formed.
Therefore, calculating 6075 using prime factorization gives us √6075 ≈ 78.
Square Root of 6075 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 6075, we need to group it as 60 and 75.
Step 2: Now we need to find n whose square is less than or equal to 60. We can say n as '7' because 7 x 7 = 49 is less than 60. Now the quotient is 7, and after subtracting 49 from 60, the remainder is 11.
Step 3: Now let us bring down 75, which is the new dividend. Add the old divisor with the same number: 7 + 7 = 14, which will be our new divisor.
Step 4: We need to find a number m such that 14m x m is less than or equal to 1175.
Step 5: By trial, we find that 147 x 7 = 1029, which is less than 1175.
Step 6: Subtract 1029 from 1175; the difference is 146.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 14600.
Step 8: Continue the long division process until the desired precision is achieved.
So the square root of √6075 is approximately 78.
Square Root of 6075 by Approximation Method
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 6075 using the approximation method.
Step 1: We have to find the closest perfect squares of √6075.
The smallest perfect square less than 6075 is 5776 (76^2), and the closest perfect square greater than 6075 is 6241 (79^2). √6075 falls between 76 and 79.
Step 2: Use the formula: (Given number - smallest perfect square) / (Next perfect square - smallest perfect square) Applying the formula: (6075 - 5776) / (6241 - 5776) = 299 / 465 ≈ 0.643
Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 76 + 0.643 = 76.643, so the square root of 6075 is approximately 76.643.
Common Mistakes and How to Avoid Them in the Square Root of 6075
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 and then move on to the second step.
For example: √(12+24) ≠ √12 + √24. The right way 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; 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 sum. This may either happen in subtracting or elsewhere.
Square Root of 6075 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6075?
The area of the square is approximately 6075 square units.
Explanation
The area of the square = side^2.
The side length is given as √6075.
Area of the square = (√6075) x (√6075) = 6075.
Therefore, the area of the square box is approximately 6075 square units.
Problem 2
A square-shaped building measuring 6075 square feet is built; if each of the sides is √6075, what will be the square feet of half of the building?
3037.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 6075 by 2, we get 3037.5.
So half of the building measures 3037.5 square feet.
Problem 3
Calculate √6075 x 3.
Approximately 234.
Explanation
The first step is to find the square root of 6075, which is approximately 78.
Then multiply 78 with 3.
So, 78 x 3 = 234.
Problem 4
What will be the square root of (6075 + 25)?
The square root is approximately 79.37.
Explanation
To find the square root, we need to find the sum of (6075 + 25). 6075 + 25 = 6100, and then √6100 ≈ 79.37.
Therefore, the square root of (6075 + 25) is approximately ±79.37.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √6075 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle is approximately 236 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√6075 + 40) = 2 × (78 + 40) = 2 × 118 = 236 units.
FAQ on Square Root of 6075
1.What is √6075 in its simplest form?
2.Mention the factors of 6075.
3.Calculate the square of 6075.
4.Is 6075 a prime number?
5.6075 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 6075?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 6075?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 6075
- 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.
- 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, known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors.
- Long division method: A method used to find the square root of a non-perfect square by dividing the number into groups of two digits, starting from the decimal point.
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About BrightChamps in United Arab Emirates
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.
