130 LearnersLast updated on May 26th, 2025
Square Root of 328
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.
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.
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
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.
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.
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.
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
Forgetting about the Negative Square Root
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.
Mistake 2
Incorrect Use of the Square Root Symbol
Misplacing the square root symbol is a common error. It's crucial to simplify numbers inside the square root before proceeding.
For example, √(12 + 24) should not be simplified to √12 + √24. The correct simplification is √36.
Mistake 3
Misestimating Non-Perfect Squares
When estimating the square root of non-perfect squares, ensure accurate approximation.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the Square Root with the Cube Root
Distinguish between square roots and cube roots.
For example, √50 and ∛50 are different operations.
Mistake 5
Errors in the Long Division Method
The long division method involves multiple steps, and missing any can lead to incorrect results. It's crucial to follow each step carefully to avoid mistakes.
Square Root of 328 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √328?
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.
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?
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.
Problem 3
Calculate √328 x 5.
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.
Problem 4
What will be the square root of (324 + 4)?
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.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √328 units and the width 'w' is 50 units.
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.
FAQ on Square Root of 328
1.What is √328 in its simplest form?
2.Mention the factors of 328.
3.Calculate the square of 328.
4.Is 328 a prime number?
5.328 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 328?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 328?
9.Does learning Algebra support future career opportunities for students in Bahrain?
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.
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About BrightChamps in Bahrain
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.
