130 LearnersLast updated on May 26th, 2025
Square Root of 3300
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 3300.
What is the Square Root of 3300?
The square root is the inverse of the square of the number. 3300 is not a perfect square. The square root of 3300 is expressed in both radical and exponential forms. In the radical form, it is expressed as √3300, whereas (3300)^(1/2) in the exponential form. √3300 ≈ 57.4456, 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 3300
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 3300 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3300 is broken down into its prime factors.
Step 1: Finding the prime factors of 3300 Breaking it down, we get 2 x 2 x 3 x 5 x 5 x 11: 2^2 x 3^1 x 5^2 x 11^1
Step 2: Now we found out the prime factors of 3300. The second step is to make pairs of those prime factors. Since 3300 is not a perfect square, therefore the digits of the number can’t be grouped into complete pairs. Therefore, calculating 3300 using prime factorization is not straightforward.
Square Root of 3300 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 3300, we need to group it as 33 and 00.
Step 2: Now we need to find n whose square is less than or equal to 33. We can say n as '5' because 5 x 5 = 25, which is less than 33. Now the quotient is 5, after subtracting 25 from 33, the remainder is 8.
Step 3: Now let us bring down 00, making the new dividend 800. Add the old divisor with the same number, 5 + 5, to get 10, which will be the start of our new divisor.
Step 4: The new divisor will be 10n, and we need to find a digit for n such that 10n x n is less than or equal to 800. Let's choose n = 7, as 107 x 7 = 749, which is less than 800.
Step 5: Subtract 749 from 800, the difference is 51.
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 zeros to the dividend. Now the new dividend is 5100.
Step 7: Continue the process with the new divisor 114 and find the next digit for n to approximate further. The quotient becomes 57.44 after several iterations.
Step 8: Continue doing these steps until we get the desired number of decimal places. So the square root of √3300 is approximately 57.4456.
Square Root of 3300 by Approximation Method
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 3300 using the approximation method.
Step 1: Now we have to find the closest perfect squares around 3300. The smallest perfect square less than 3300 is 3249 (57^2) and the largest perfect square greater than 3300 is 3364 (58^2). Therefore, √3300 falls between 57 and 58.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Applying the formula: (3300 - 3249) / (3364 - 3249) = 51 / 115 ≈ 0.4435 Using the formula, we identify the decimal approximation of our square root. The next step is adding the integer part, so 57 + 0.4435 ≈ 57.445. So the square root of 3300 is approximately 57.445.
Common Mistakes and How to Avoid Them in the Square Root of 3300
Students do make mistakes while finding the square root, such as forgetting about the negative square root or 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: √3300 ≈ 57.4456, there is also -57.4456 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: √(25 + 100) = √25 + √100 is an incorrect method of using roots. The right way of using roots is √(25 + 100) = √125.
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: √3300 ≈ 57 is wrong; the correct answer is √3300 ≈ 57.4456.
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 avoid mistakes.
For example: √3300 and ∛3300 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 sum. This may either happen in subtracting or elsewhere.
Square Root of 3300 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3300?
The area of the square is 3300 square units.
Explanation
The area of the square = side^2.
The side length is given as √3300.
Area of the square = side^2 = √3300 x √3300 = 3300.
Therefore, the area of the square box is 3300 square units.
Problem 2
A square-shaped building measuring 3300 square feet is built; if each of the sides is √3300, what will be the square feet of half of the building?
1650 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3300 by 2 = 1650.
So half of the building measures 1650 square feet.
Problem 3
Calculate √3300 x 5.
287.228
Explanation
The first step is to find the square root of 3300, which is approximately 57.4456.
The second step is to multiply 57.4456 by 5.
So 57.4456 x 5 ≈ 287.228.
Problem 4
What will be the square root of (3200 + 100)?
The square root is 57.
Explanation
To find the square root, we need to find the sum of (3200 + 100).
3200 + 100 = 3300, and then √3300 ≈ 57.
Therefore, the square root of (3200 + 100) is approximately 57.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3300 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 214.8912 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3300 + 50) ≈ 2 × (57.4456 + 50) ≈ 2 × 107.4456 ≈ 214.8912 units.
FAQ on Square Root of 3300
1.What is √3300 in its simplest form?
2.Mention the factors of 3300.
3.Calculate the square of 3300.
4.Is 3300 a prime number?
5.3300 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 3300?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 3300?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 3300
- Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: Prime factorization is expressing a number as a product of its prime factors. For example, the prime factorization of 30 is 2 x 3 x 5.
- Long division method: The long division method is a technique for dividing numbers to find the remainder and quotient, particularly used in finding the square roots of non-perfect squares.
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Jaskaran Singh Saluja
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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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