103 LearnersLast updated on May 26th, 2025
Square Root of 3.33
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 field of vehicle design, finance, etc. Here, we will discuss the square root of 3.33.
What is the Square Root of 3.33?
The square root is the inverse of the square of the number. 3.33 is not a perfect square. The square root of 3.33 is expressed in both radical and exponential form. In the radical form, it is expressed as √3.33, whereas (3.33)^(1/2) in the exponential form. √3.33 ≈ 1.8248, 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 3.33
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 3.33 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 3.33, we consider it as 3.33.
Step 2: Now we need to find n whose square is close to 3. We can say n is '1' because 1 × 1 is lesser than or equal to 3. Now the quotient is 1 and the remainder is 3 - 1 = 2.
Step 3: Bring down the next pair of digits, which is 33, making the new dividend 233. Double the quotient and bring it down as the new divisor, so 2 × 1 = 2.
Step 4: The new divisor is now 20 + n, where n is chosen such that (20 + n) × n ≤ 233. The value of n is 8.
Step 5: Subtract 208 from 233 to get the remainder 25. The quotient is now 1.8.
Step 6: Since we need more precision, bring down two zeroes to make it 2500.
Step 7: The new divisor is 36, and we need to choose n such that (360 + n) × n ≤ 2500. The value of n is 6.
Step 8: Subtract 2196 from 2500, giving a remainder of 304.
Step 9: The quotient is now 1.824.
Step 10: Continue with these steps until the desired precision is achieved or the remainder is zero.
So the square root of √3.33 ≈ 1.8248.
Square Root of 3.33 by Approximation Method
The approximation method is another method for finding square roots, and 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 3.33 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √3.33. The smallest perfect square less than 3.33 is 1 (1²) and the largest perfect square greater than 3.33 is 4 (2²). √3.33 falls somewhere between 1 and 2.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (3.33 - 1) ÷ (4 - 1) = 2.33 ÷ 3 ≈ 0.7767. Using the formula, we identified the decimal part of our square root. The next step is adding the integer part, which is 1, to the decimal number: 1 + 0.7767 ≈ 1.7767.
Therefore, the square root of 3.33 is approximately 1.7767.
Common Mistakes and How to Avoid Them in the Square Root of 3.33
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students that a number has both positive and negative square roots. However, we usually consider only the positive square root for practical purposes.
For example: √50 = 7.07, but there is also -7.07, which should not be forgotten.
Square Root of 3.33 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3.33?
The area of the square is approximately 11.07 square units.
Explanation
The area of the square = side².
The side length is given as √3.33.
Area of the square = (√3.33)² = 3.33.
Therefore, the area of the square box is approximately 11.07 square units.
Problem 2
A square-shaped building measuring 3.33 square meters is built; if each side is √3.33, what will be the area of half the building?
1.665 square meters
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 3.33 by 2 gives us 1.665.
So half of the building measures 1.665 square meters.
Problem 3
Calculate √3.33 × 5.
Approximately 9.124
Explanation
The first step is to find the square root of 3.33, which is approximately 1.8248.
The second step is to multiply 1.8248 by 5.
So 1.8248 × 5 ≈ 9.124.
Problem 4
What will be the square root of (3.33 + 1)?
The square root is approximately 2.16.
Explanation
To find the square root, we need to find the sum of (3.33 + 1). 3.33 + 1 = 4.33, then √4.33 ≈ 2.08.
Therefore, the square root of (3.33 + 1) is approximately 2.08.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3.33 units and the width ‘w’ is 3 units.
We find the perimeter of the rectangle as approximately 9.65 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3.33 + 3) ≈ 2 × (1.8248 + 3) ≈ 2 × 4.8248 ≈ 9.65 units.
FAQ on Square Root of 3.33
1.What is √3.33 in its simplest form?
2.Is 3.33 a perfect square?
3.Calculate the square of 3.33.
4.Is 3.33 a rational number?
5.3.33 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 3.33?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 3.33?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 3.33
- Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse is the square root, so √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction, such as √3.33.
- Rational number: A rational number can be expressed as a fraction of two integers, such as 3.33 = 333/100.
- Principal square root: The non-negative square root of a number is called the principal square root. For example, the principal square root of 3.33 is 1.8248.
- Decimal: A decimal number includes a whole number and a fractional part, such as 3.33.
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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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