Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √6052 x 5.
389.1
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.
What will be the square root of (6052 + 100)?
The square root is approximately 78.48.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√6052 + 50) ≈ 2 × (77.82 + 50) ≈ 2 × 127.82 ≈ 255.64 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.