112 LearnersLast updated on May 26th, 2025
Square Root of 6052
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 6052.
What is the Square Root of 6052?
The square root is the inverse of the square of the number. 6052 is not a perfect square. The square root of 6052 is expressed in both radical and exponential form. In the radical form, it is expressed as √6052, whereas (6052)^(1/2) in the exponential form. √6052 ≈ 77.82, 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 6052
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 6052 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6052 is broken down into its prime factors.
Step 1: Finding the prime factors of 6052 Breaking it down, we get 2 x 2 x 1513: 2^2 x 1513^1
Step 2: Now we found out the prime factors of 6052. The second step is to make pairs of those prime factors. Since 6052 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating 6052 using prime factorization alone is not straightforward.
Square Root of 6052 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 6052, we need to group it as 52 and 60.
Step 2: Now we need to find a number 'n' whose square is less than or equal to 60. We can say n is '7' because 7 x 7 = 49, which 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 52, making the new dividend 1152. Add the old divisor with the same number 7 + 7 = 14, which will be our new divisor.
Step 4: The new divisor is 14n. We need to find the value of n such that 14n x n is less than or equal to 1152.
Step 5: By trial and error, we find n = 8 because 148 x 8 = 1184, which exceeds 1152, so we use n = 7.
Step 6: Subtract 1029 from 1152, the difference is 123, and the quotient is 77.
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 12300.
Step 8: Continue with the long division steps to find the precise decimal value until you reach the required precision.
So the square root of √6052 is approximately 77.82.
Square Root of 6052 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 6052 using the approximation method.
Step 1: Now we have to find the closest perfect square of √6052.
The smallest perfect square less than 6052 is 5929 (77^2) and the largest perfect square greater than 6052 is 6084 (78^2). √6052 falls somewhere between 77 and 78.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula, (6052 - 5929) / (6084 - 5929) = 123 / 155 ≈ 0.7935.
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 77 + 0.7935 ≈ 77.79, so the square root of 6052 is approximately 77.79.
Common Mistakes and How to Avoid Them in the Square Root of 6052
Students may 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 has 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 symbol 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 next step.
For example, √(12+24) = √12 + √24 is a 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 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the 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 happen during subtraction or elsewhere.
Square root of 6052 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6052?
The area of the square is approximately 36,624.64 square units.
Explanation
The area of the square = side^2.
The side length is given as √6052.
Area of the square = side^2 = √6052 x √6052 ≈ 77.82 x 77.82 ≈ 36,624.64.
Therefore, the area of the square box is approximately 36,624.64 square units.
Problem 2
A square-shaped building measuring 6052 square feet is built; if each of the sides is √6052, what will be the square feet of half of the building?
3026 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 6052 by 2 = 3026.
So, half of the building measures 3026 square feet.
Problem 3
Calculate √6052 x 5.
389.1
Explanation
The first step is to find the square root of 6052, which is approximately 77.82.
The second step is to multiply 77.82 by 5.
So, 77.82 x 5 = 389.1.
Problem 4
What will be the square root of (6052 + 100)?
The square root is approximately 78.48.
Explanation
To find the square root, we need to find the sum of (6052 + 100). 6052 + 100 = 6152, and then √6152 ≈ 78.48.
Therefore, the square root of (6052 + 100) is approximately ±78.48.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √6052 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 255.64 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√6052 + 50) ≈ 2 × (77.82 + 50) ≈ 2 × 127.82 ≈ 255.64 units.
FAQ on Square Root of 6052
1.What is √6052 in its simplest form?
2.Mention the factors of 6052.
3.Calculate the square of 6052.
4.Is 6052 a prime number?
5.6052 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 6052?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 6052?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 6052
- 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. That is why it is also known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 12 is 2 x 2 x 3.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
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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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