103 LearnersLast updated on May 26th, 2025
Square Root of 2.5
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 2.5.
What is the Square Root of 2.5?
The square root is the inverse of the square of the number. 2.5 is not a perfect square. The square root of 2.5 is expressed in both radical and exponential form. In radical form, it is expressed as √2.5, whereas (2.5)^(1/2) in exponential form. √2.5 ≈ 1.58114, 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 2.5
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 2.5, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 2.5 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 express the number as 2.50 to facilitate division.
Step 2: Find the closest perfect square less than or equal to 2.5, which is 1. Now, 1 × 1 = 1. Subtract 1 from 2.5, giving 1.5.
Step 3: Double the result from step 2, which is 1, to get 2.
Step 4: Bring down two zeros to make it 150. Find a digit n such that 2n × n is less than or equal to 150. The digit n is 5, as 25 × 5 = 125.
Step 5: Subtract 125 from 150, leaving a remainder of 25.
Step 6: Bring down another pair of zeros to get 2500. Repeat the process to get a more accurate result.
Step 7: The square root of 2.5 is approximately 1.58114.
Square Root of 2.5 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 2.5 using the approximation method.
Step 1: Identify the closest perfect squares around 2.5, which are 1 (1^2) and 4 (2^2). √2.5 falls between 1 and 2.
Step 2: Use interpolation to approximate: 2.5 is closer to 4 than to 1, so we estimate a value closer to 1.6.
Step 3: Calculate and refine to find the approximate value: The square root of 2.5 ≈ 1.58.
Common Mistakes and How to Avoid Them in the Square Root of 2.5
Students can make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of those mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we usually take only the positive square root, as it is the required one.
For example: √2.5 ≈ 1.58114, but there is also -1.58114 which should not be forgotten.
Square Root of 2.5 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2.5?
The area of the square is approximately 6.25 square units.
Explanation
The area of the square = side^2.
The side length is given as √2.5.
Area of the square = (√2.5) × (√2.5) ≈ 1.58114 × 1.58114 ≈ 2.5.
Therefore, the area of the square box is approximately 2.5 square units.
Problem 2
A square-shaped building measuring 2.5 square feet is built; if each of the sides is √2.5, what will be the square feet of half of the building?
1.25 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2.5 by 2, we get 1.25.
So half of the building measures 1.25 square feet.
Problem 3
Calculate √2.5 × 5.
Approximately 7.9057
Explanation
The first step is to find the square root of 2.5, which is approximately 1.58114.
The second step is to multiply 1.58114 by 5.
So, 1.58114 × 5 ≈ 7.9057.
Problem 4
What will be the square root of (2 + 0.5)?
The square root is approximately 1.58114.
Explanation
To find the square root, we need to find the sum of (2 + 0.5). 2 + 0.5 = 2.5, and then √2.5 ≈ 1.58114.
Therefore, the square root of (2 + 0.5) is approximately ±1.58114.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √2.5 units and the width 'w' is 3 units.
The perimeter of the rectangle is approximately 9.16228 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2.5 + 3) ≈ 2 × (1.58114 + 3) ≈ 2 × 4.58114 ≈ 9.16228 units.
FAQ on Square Root of 2.5
1.What is √2.5 in its simplest form?
2.Is 2.5 a perfect square?
3.Calculate the square of 2.5.
4.Is 2.5 a prime number?
5.What are the factors of 2.5?
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 2.5?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 2.5?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 2.5
- Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: √4 = 2, since 2 × 2 = 4.
- Irrational number: An irrational number cannot be written as a simple fraction, and its decimal form is non-repeating and non-terminating.
- Approximation method: A method to estimate the square root by identifying the closest perfect squares and using interpolation.
- Long division method: A step-by-step way to find the square root of a number by dividing, multiplying, and subtracting.
- Decimal: A number that includes a whole number and a fractional part separated by a decimal point, such as 1.58114.
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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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