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Last updated on May 26th, 2025

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Square Root of 328

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If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. Square roots are used in various fields like vehicle design and finance. Here, we will discuss the square root of 328.

Square Root of 328 for US Students
Professor Greenline from BrightChamps

What is the Square Root of 328?

The square root is the inverse of squaring a number. 328 is not a perfect square. The square root of 328 can be expressed in both radical and exponential forms. In radical form, it is expressed as √328, whereas in exponential form it is (328)^(1/2). √328 ≈ 18.11077, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

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Finding the Square Root of 328

The prime factorization method is used for perfect square numbers. However, for non-perfect squares like 328, the long division and approximation methods are commonly used. Let us now explore these methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 328 by Prime Factorization Method

The prime factorization of a number is the product of its prime factors. Let's see how 328 can be broken down into its prime factors:

 

Step 1: Finding the prime factors of 328 Breaking it down, we get 2 x 2 x 2 x 41: 2^3 x 41

 

Step 2: Since 328 is not a perfect square, we cannot pair all the prime factors.

 

Therefore, calculating √328 using prime factorization directly is not feasible.

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Square Root of 328 by Long Division Method

The long division method is effective for non-perfect squares. Here's how to find the square root using this method, step by step:

 

Step 1: Group the digits of 328 from right to left as 28 and 3.

 

Step 2: Find the largest number whose square is less than or equal to 3. This number is 1 since 1 x 1 = 1. Subtract 1 from 3 to get a remainder of 2.

 

Step 3: Bring down the next group of digits, 28, to get a new dividend of 228.

 

Step 4: Double the quotient (1) to get 2, which becomes the new divisor prefix.

 

Step 5: Find a digit n such that 2n x n is less than or equal to 228. Here, n is 8, since 28 x 8 = 224.

 

Step 6: Subtract 224 from 228 to get a remainder of 4. The quotient is now 18.

 

Step 7: Add a decimal point to the quotient and bring down two zeros to make the new dividend 400.

 

Step 8: Double the current quotient (18) to get 36, and find n such that 36n x n is less than or equal to 400. Here, n is 1, since 361 x 1 = 361.

 

Step 9: Subtract 361 from 400 to get a remainder of 39.

 

Step 10: The quotient is now 18.1. Continue the process to get more decimal places as needed.

 

The approximate value of √328 is 18.11.

Professor Greenline from BrightChamps

Square Root of 328 by Approximation Method

The approximation method is another way to find square roots. Here's how to use it for 328:

 

Step 1: Identify the closest perfect squares around √328.

 

The closest perfect squares are 324 (18^2) and 361 (19^2). Thus, √328 is between 18 and 19.

 

Step 2: Use the formula (Given number - lower perfect square) / (higher perfect square - lower perfect square) to find the decimal. (328 - 324) / (361 - 324) = 4 / 37 ≈ 0.108 Adding this to 18 gives 18 + 0.108 ≈ 18.108.

 

Therefore, the square root of 328 is approximately 18.11.

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Common Mistakes and How to Avoid Them in the Square Root of 328

Students often make mistakes while finding square roots, such as overlooking the negative square root or skipping steps in the long division method. Here are a few common errors students make:

Mistake 1

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Forgetting about the Negative Square Root

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It's important to remember that every positive number has both a positive and a negative square root. However, we typically consider only the positive square root in practical applications.

For example: √50 ≈ 7.07, but there's also -7.07.

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Square Root of 328 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √328?

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The area of the square is approximately 328 square units.

Explanation

The area of a square is side^2.

The side length is given as √328.

Area = side^2 = √328 x √328 = 328.

Therefore, the area of the square box is approximately 328 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 328 square feet is built. If each of the sides is √328, what will be the square feet of half of the building?

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164 square feet

Explanation

Since the building is square-shaped, simply divide the given area by 2.

Dividing 328 by 2 gives 164.

So, half of the building measures 164 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √328 x 5.

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Approximately 90.55

Explanation

First, find the square root of 328, which is approximately 18.11.

Then multiply this by 5.

So, 18.11 x 5 ≈ 90.55.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (324 + 4)?

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The square root is 18.

Explanation

To find the square root, add the numbers (324 + 4) to get 328, then find the square root of 328, which is approximately 18.11. Therefore, the square root of (324 + 4) is approximately 18.11.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length 'l' is √328 units and the width 'w' is 50 units.

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The perimeter of the rectangle is approximately 136.22 units.

Explanation

Perimeter of a rectangle = 2 × (length + width).

Perimeter = 2 × (√328 + 50) = 2 × (18.11 + 50) = 2 × 68.11 = 136.22 units.

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FAQ on Square Root of 328

1.What is √328 in its simplest form?

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2.Mention the factors of 328.

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3.Calculate the square of 328.

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4.Is 328 a prime number?

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5.328 is divisible by?

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6.How does learning Algebra help students in United States make better decisions in daily life?

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7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 328?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 328?

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9.Does learning Algebra support future career opportunities for students in United States?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 328

  • Square root: A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4^2 = 16.

 

  • Irrational number: An irrational number cannot be expressed as a simple fraction. Examples include √2 and π.

 

  • Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4^2.

 

  • Long division method: A technique used to find the square root of non-perfect squares through a step-by-step division process.

 

  • Approximation method: A method used to estimate the square root of a number by identifying nearby perfect squares and using linear interpolation.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of 328, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. Let’s make square roots an exciting part of every child’s math adventure!
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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.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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