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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 3280.
The square root is the inverse of the square of the number. 3280 is not a perfect square. The square root of 3280 is expressed in both radical and exponential form. In radical form, it is expressed as √3280, whereas in exponential form it is expressed as (3280)^(1/2). √3280 ≈ 57.276, 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 3280 is broken down into its prime factors.
Step 1: Finding the prime factors of 3280 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 41: 2^4 x 5 x 41
Step 2: Now we have found the prime factors of 3280. The second step is to make pairs of those prime factors. Since 3280 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 3280 using prime factorization 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 3280, we group it as 80 and 32.
Step 2: Now we need to find n whose square is less than or equal to 32. We can say n is '5' because 5 x 5 = 25 is less than 32. Now the quotient is 5, and after subtracting 25 from 32, the remainder is 7.
Step 3: Now let us bring down 80 which is the new dividend. Add the old divisor with the same number 5 + 5 = 10, which will be our new divisor.
Step 4: The new divisor will be 10n. We need to find the largest n such that 10n x n ≤ 780. Let's consider n as 7, now 107 x 7 = 749.
Step 5: Subtracting 749 from 780, the difference is 31, and the quotient is 57.
Step 6: 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 3100.
Step 7: Now we need to find the new divisor that is 574 because 574 x 4 = 2296.
Step 8: Subtracting 2296 from 3100, we get the result 804.
Step 9: Continue doing these steps until we get two numbers after the decimal point. So the square root of √3280 is approximately 57.28.
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 3280 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3280. The smallest perfect square less than 3280 is 3249 (57^2) and the largest perfect square less than 3280 is 3364 (58^2). √3280 falls somewhere between 57 and 58.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the approximation formula (3280 - 3249) / (3364 - 3249) = 31 / 115 ≈ 0.2696 Adding this to the smaller root, we get 57 + 0.2696 = 57.2696. Therefore, the approximate square root of 3280 is 57.27.
Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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 √3280?
The area of the square is 3280 square units.
The area of the square = side^2.
The side length is given as √3280.
Area of the square = side^2 = √3280 x √3280 = 3280.
Therefore, the area of the square box is 3280 square units.
A square-shaped building measuring 3280 square feet is built; if each of the sides is √3280, what will be the square feet of half of the building?
1640 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3280 by 2, we get 1640.
So half of the building measures 1640 square feet.
Calculate √3280 x 5.
Approximately 286.38
The first step is to find the square root of 3280, which is approximately 57.28.
The second step is to multiply 57.28 by 5.
So 57.28 x 5 ≈ 286.38.
What will be the square root of (3280 + 20)?
The square root is approximately 57.618.
To find the square root, we need to find the sum of (3280 + 20).
3280 + 20 = 3300, and then √3300 ≈ 57.618.
Therefore, the square root of (3280 + 20) is ±57.618.
Find the perimeter of the rectangle if its length ‘l’ is √3280 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 190.56 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3280 + 38) = 2 × (57.28 + 38) = 2 × 95.28 = 190.56 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.