131 LearnersLast updated on May 26th, 2025
Square Root of 330
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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 330.
What is the Square Root of 330?
The square root is the inverse of the square of the number. 330 is not a perfect square. The square root of 330 is expressed in both radical and exponential form. In the radical form, it is expressed as √330, whereas (330)^(1/2) in the exponential form. √330 ≈ 18.1659, 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 330
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 330 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 330 is broken down into its prime factors.
Step 1: Finding the prime factors of 330 Breaking it down, we get 2 x 3 x 5 x 11: 2^1 x 3^1 x 5^1 x 11^1
Step 2: Since 330 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating the square root of 330 using prime factorization is not straightforward.
Square Root of 330 by Long Division Method
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 330, we need to group it as 30 and 3.
Step 2: Now we need to find n whose square is less than or equal to 3. We can say n is ‘1’ because 1 x 1 is less than or equal to 3. Now the quotient is 1; after subtracting 1 from 3, the remainder is 2.
Step 3: Now let us bring down 30, which is the new dividend. Add the old divisor with the same number 1 + 1, which gives us 2 as the new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 230. Let us consider n as 8, now 28 x 8 = 224.
Step 6: Subtract 224 from 230, the difference is 6, and the quotient is 18.
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 600.
Step 8: Now we need to find the new divisor that is 181 because 181 x 3 = 543.
Step 9: Subtracting 543 from 600, we get the result 57.
Step 10: Now the quotient is 18.1
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue until the remainder is zero.
So the square root of √330 is approximately 18.16.
Square Root of 330 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 330 using the approximation method.
Step 1: Now we have to find the closest perfect square of √330.
The smallest perfect square less than 330 is 324, and the largest perfect square greater than 330 is 361. √330 falls somewhere between 18 and 19.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (330 - 324) / (361 - 324) = 6 / 37 ≈ 0.162
Using the formula, we identified the decimal part of our square root. The next step is adding the value we got initially to the decimal number which is 18 + 0.162 = 18.162, so the square root of 330 is approximately 18.162.
Common Mistakes and How to Avoid Them in the Square Root of 330
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12 + 24) = √12 + √24 is the wrong method of using roots. The right way of using roots is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong, the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them keep away from mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the problem. This may either happen in subtraction or elsewhere.
Square Root of 330 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √330?
The area of the square is approximately 330 square units.
Explanation
The area of the square = side^2.
The side length is given as √330.
Area of the square = side^2 = √330 x √330 = 330.
Therefore, the area of the square box is approximately 330 square units.
Problem 2
A square-shaped building measuring 330 square feet is built; if each of the sides is √330, what will be the square feet of half of the building?
165 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 330 by 2, we get 165.
So half of the building measures 165 square feet.
Problem 3
Calculate √330 x 5.
Approximately 90.83
Explanation
The first step is to find the square root of 330, which is approximately 18.16.
The second step is to multiply 18.16 by 5.
So 18.16 x 5 = approximately 90.83.
Problem 4
What will be the square root of (300 + 30)?
The square root is approximately 18.1659.
Explanation
To find the square root, we need to find the sum of (300 + 30). 300 + 30 = 330, and then √330 ≈ 18.1659.
Therefore, the square root of (300 + 30) is approximately ±18.1659.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √330 units and the width ‘w’ is 30 units.
The perimeter of the rectangle is approximately 96.33 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√330 + 30) = 2 × (18.1659 + 30) ≈ 2 × 48.1659 ≈ 96.33 units.
FAQ on Square Root of 330
1.What is √330 in its simplest form?
2.Mention the factors of 330.
3.Calculate the square of 330.
4.Is 330 a prime number?
5.330 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 330?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 330?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 330
- Square root: A square root is the inverse of squaring a number. Example: 4^2 = 16 and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Approximation: Approximation is a method used to find a value that is close enough to the right answer, typically with less effort.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors.
- Decimal: A decimal is a number that includes a whole number and a fraction in a single number, for example, 7.86, 8.65, and 9.42.
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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
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