Square Root of 3328
2026-02-28 10:16 Diff
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Last updated on August 5, 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 various fields including vehicle design and finance. Here, we will discuss the square root of 3328.

What is the Square Root of 3328?

The square root is the inverse of the square of a number. 3328 is not a perfect square. The square root of 3328 is expressed in both radical and exponential form. In the radical form, it is expressed as √3328, whereas in exponential form it is expressed as (3328)^(1/2). √3328 ≈ 57.693, 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 3328

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 3328 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3328 is broken down into its prime factors:

Step 1: Finding the prime factors of 3328 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 13: 2^6 x 13

Step 2: Now we have found the prime factors of 3328. The next step is to make pairs of those prime factors. Since 3328 is not a perfect square, the digits of the number can’t be grouped into pairs evenly. Therefore, calculating the square root of 3328 using prime factorization is not straightforward.

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Square Root of 3328 by Long Division Method

The long division method is particularly useful 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 digits from right to left in pairs. For 3328, we consider 28 and 33.

Step 2: Now, find n whose square is less than or equal to 33. We can take n as 5 because 5^2 = 25, which is less than 33. The quotient is 5, and after subtraction, 33 - 25 = 8.

Step 3: Bring down the next pair of digits, which is 28, to make the new dividend, 828.

Step 4: Add the previous divisor (5) to itself to get 10, and use this as a part of the new divisor.

Step 5: Find a new digit p such that 10p x p is less than or equal to 828. In this case, 107 x 7 = 749.

Step 6: Subtract 749 from 828 to get 79. The quotient is now 57.

Step 7: Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend making it 7900.

Step 8: The new divisor is 1149 (1070 + 7 + 7). Find a digit q such that 1149q x q is less than or equal to 7900. Continue this process until you achieve the desired precision. The square root of 3328 is approximately 57.69.

Square Root of 3328 by Approximation Method

The approximation method is another way to find 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 3328 using the approximation method.

Step 1: Identify the nearest perfect squares for 3328. The smallest perfect square less than 3328 is 3249 (57^2) and the largest perfect square more than 3328 is 3364 (58^2). Thus, √3328 falls between 57 and 58.

Step 2: Apply the formula: (Given number - smallest perfect square) / (greater perfect square - smallest perfect square). Using the formula (3328 - 3249) / (3364 - 3249) ≈ 0.69 Add this decimal to the smaller integer value, which is 57. Therefore, 57 + 0.69 = 57.69. The approximate square root of 3328 is 57.69.

Common Mistakes and How to Avoid Them in the Square Root of 3328

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √3328?

Okay, lets begin

The area of the square is approximately 3328 square units.

Explanation

The area of a square is calculated as side^2.

The side length is given as √3328.

Area of the square = (√3328) x (√3328) = 3328.

Therefore, the area of the square box is approximately 3328 square units.

Well explained 👍

Problem 2

A square-shaped garden measures 3328 square feet in area; if each of the sides is √3328, what will be the area of half of the garden?

Okay, lets begin

The area of half of the garden is 1664 square feet.

Explanation

We can divide the total area by 2, as the garden is square-shaped.

Dividing 3328 by 2 gives us 1664.

So half of the garden measures 1664 square feet.

Well explained 👍

Problem 3

Calculate √3328 x 3.

Okay, lets begin

The result is approximately 173.079.

Explanation

First, find the square root of 3328, which is approximately 57.693. Then, multiply 57.693 by 3. So, 57.693 x 3 ≈ 173.079.

Well explained 👍

Problem 4

What will be the square root of (3328 + 72)?

Okay, lets begin

The square root is approximately 58.

Explanation

To find the square root, first calculate the sum of (3328 + 72). 3328 + 72 = 3400.

The approximate square root of 3400 is 58.

Therefore, the square root of (3328 + 72) is approximately ±58.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √3328 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is approximately 215.386 units.

Explanation

The perimeter of a rectangle is calculated as 2 × (length + width). Perimeter = 2 × (√3328 + 50) ≈ 2 × (57.693 + 50) = 2 × 107.693 ≈ 215.386 units.

Well explained 👍

FAQ on Square Root of 3328

1.What is √3328 in its simplest form?

The prime factorization of 3328 is 2^6 x 13, so the simplest radical form of √3328 is 2^3√13.

2.What are the factors of 3328?

The factors of 3328 are 1, 2, 4, 8, 16, 32, 64, 104, 208, 416, 832, 1664, and 3328.

3.Calculate the square of 3328.

The square of 3328 is obtained by multiplying the number by itself: 3328 x 3328 = 11059264.

4.Is 3328 a prime number?

3328 is not a prime number, as it has more than two factors.

5.What numbers is 3328 divisible by?

3328 is divisible by 1, 2, 4, 8, 16, 32, 64, 104, 208, 416, 832, 1664, and 3328.

Important Glossaries for the Square Root of 3328

  • Square root: A square root is the inverse of squaring a number. Example: If 8^2 = 64, then the inverse, or square root, is √64 = 8.
  • Irrational number: An irrational number cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.
  • Principal square root: The principal square root of a number is its non-negative square root, often used in real-world applications.
  • Prime factorization: The process of breaking down a number into its basic prime factors.
  • Long division method: A systematic approach to finding the square root of numbers, especially useful for non-perfect squares.

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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.