101 LearnersLast updated on May 26th, 2025
Square Root of 3.25
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 mathematics, engineering, and science. Here, we will discuss the square root of 3.25.
What is the Square Root of 3.25?
The square root is the inverse of the square of a number. 3.25 is not a perfect square. The square root of 3.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √3.25, whereas (3.25)^(1/2) in the exponential form. √3.25 ≈ 1.80278, 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 3.25
The prime factorization method is more suitable for perfect square numbers. However, for non-perfect square numbers like 3.25, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 3.25 by Long Division Method
The long division method is particularly effective for non-perfect square numbers. In this method, we focus on finding the square root through a series of steps.
Step 1: To begin, set the number 3.25 in decimal form and consider it as 325.
Step 2: Pair the digits starting from the decimal point. In this case, we have 3.25, so the pair is 32 and 5.
Step 3: Find a number whose square is less than or equal to 3. The number is 1 because 1 × 1 ≤ 3.
Step 4: Subtract 1² from 3 to get the remainder 2, and bring down 2 to make it 22.
Step 5: Double the divisor (1) to get 2 and find a digit to append to 2 to make it less than or equal to 225. That digit is 8 because 28 × 8 = 224.
Step 6: Subtract 224 from 225 to get the remainder 1. Bring down 00 to make it 100.
Step 7: Double the divisor 18 to get 36 and determine a digit to append to 36 to make it less than or equal to 100. That digit is 2 because 362 × 2 = 724.
Step 8: Continue this process until the desired precision is achieved.
The result is approximately 1.80278.
Square Root of 3.25 by Approximation Method
The approximation method is another approach for finding square roots. It involves estimating the value based on nearby perfect squares.
Step 1: Identify the nearest perfect squares surrounding 3.25. The closest perfect squares are 1 (1²) and 4 (2²), so √3.25 is between 1 and 2.
Step 2: Use interpolation to approximate the value. Given that 3.25 is closer to 4 than to 1, we can estimate the square root is closer to 2.
Step 3: Using the formula (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square), we get: (3.25 - 1) / (4 - 1) = 2.25 / 3 ≈ 0.75
Step 4: Adding this to the lower boundary value gives us 1 + 0.75 = 1.75.
Adjusting through trial and error, we find that √3.25 ≈ 1.80278.
Mistakes in Calculating the Square Root of 3.25
When calculating the square root, students might make errors such as omitting the negative square root or misplacing the decimal point. Let's explore some common mistakes in detail.
Mistake 1
Forgetting about the Negative Square Root
It's crucial to remind students that a number has both positive and negative square roots. However, we typically consider only the positive square root in most real-world applications.
For example, √3.25 = ±1.80278, but we generally use the positive 1.80278.
Square Root of 3.25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3.25?
The area of the square is approximately 10.5601 square units.
Explanation
The area of the square = side².
The side length is given as √3.25 ≈ 1.80278.
Area = (√3.25)² = 1.80278 × 1.80278 ≈ 3.25.
Therefore, the area of the square box is approximately 3.25 square units.
Problem 2
A square-shaped garden measuring 3.25 square meters is built; if each of the sides is √3.25, what will be the square meters of half of the garden?
1.625 square meters
Explanation
We can divide the given area by 2 since the garden is square-shaped.
Dividing 3.25 by 2, we get 1.625.
So, half of the garden measures 1.625 square meters.
Problem 3
Calculate √3.25 × 5.
Approximately 9.0139
Explanation
First, find the square root of 3.25, which is approximately 1.80278.
Then, multiply 1.80278 by 5.
So 1.80278 × 5 ≈ 9.0139.
Problem 4
What will be the square root of (2 + 1.25)?
The square root is approximately 1.80278.
Explanation
To find the square root, we compute the sum of (2 + 1.25), which totals 3.25. √3.25 ≈ 1.80278.
Therefore, the square root of (2 + 1.25) is approximately 1.80278.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3.25 units and the width ‘w’ is 5 units.
The perimeter of the rectangle is approximately 13.6056 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3.25 + 5) ≈ 2 × (1.80278 + 5) ≈ 2 × 6.80278 ≈ 13.6056 units.
FAQ on Square Root of 3.25
1.What is √3.25 in its simplest form?
2.Is 3.25 a perfect square?
3.Calculate the square of 3.25.
4.Is 3.25 a rational number?
5.What is the decimal expansion of √3.25?
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 3.25?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 3.25?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 3.25
- Square root: A square root is a number that, when multiplied by itself, gives the original number. Example: √9 = 3.
- Irrational number: An irrational number cannot be expressed as a simple fraction. Its decimal expansion is non-repeating and non-terminating
- Approximation: An approximation is an estimated value close to the actual value. Often used for irrational numbers.
- Decimal: A decimal represents a fraction using powers of ten, such as 0.5 or 3.25.
- Long division method: A technique used for finding square roots of non-perfect squares by dividing the number into pairs of digits and estimating step by step.
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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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