102 LearnersLast updated on May 26th, 2025
Square Root of 2.73
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 2.73.
What is the Square Root of 2.73?
The square root is the inverse of the square of the number. 2.73 is not a perfect square. The square root of 2.73 is expressed in both radical and exponential form. In the radical form, it is expressed as √2.73, whereas (2.73)^(1/2) in the exponential form. √2.73 ≈ 1.652891, 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 2.73
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2.73 by Prime Factorization Method
The prime factorization method is not applicable to find the square root of non-perfect squares like 2.73. Instead, we can use methods like the long division method to find the approximate value of the square root.
Square Root of 2.73 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, pair the numbers starting from the decimal point. Here, we consider 2.73.
Step 2: Determine the number whose square is closest to 2 without exceeding it. The number is 1 as 1 × 1 = 1. Subtract 1 from 2 to get the remainder 1.
Step 3: Bring down 73 to make it 173. Add the previous divisor (1) to itself to get the new divisor (2).
Step 4: Find a number n such that 2n × n ≤ 173. The number is 6, as 26 × 6 = 156.
Step 5: Subtract 156 from 173 to get the remainder 17.
Step 6: Since the dividend is less than the divisor, add a decimal point and bring down two zeros, making it 1700.
Step 7: The process is repeated to find the next digits of the square root. Continue this process to find the square root up to the desired decimal places.
The square root of 2.73 is approximately 1.652891.
Square Root of 2.73 by Approximation Method
Approximation method is another method for finding the 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 2.73 using the approximation method.
Step 1: Identify the closest perfect squares around 2.73. The smallest perfect square is 1 (√1 = 1), and the largest perfect square is 4 (√4 = 2).
Step 2: The square root of 2.73 falls between 1 and 2.
Step 3: Estimate the square root more closely using trial and error or interpolation.
Knowing that √2.73 is closer to √4, we find it is approximately 1.652891.
Common Mistakes and How to Avoid Them in the Square Root of 2.73
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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 typically take only the positive square root, as it is usually the desired one.
For example, √2.73 ≈ 1.652891, but there is also -1.652891, which should not be forgotten.
Square Root of 2.73 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2.73?
The area of the square is approximately 7.452 square units.
Explanation
The area of the square = side^2.
The side length is given as √2.73.
Area of the square = (√2.73) × (√2.73) ≈ 1.652891 × 1.652891 ≈ 2.73.
Problem 2
A square-shaped building measures 2.73 square meters in area. If each of the sides is √2.73, what will be the square meters of half of the building?
1.365 square meters
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2.73 by 2 = 1.365.
So half of the building measures 1.365 square meters.
Problem 3
Calculate √2.73 × 5.
Approximately 8.264455
Explanation
The first step is to find the square root of 2.73, which is approximately 1.652891.
The second step is to multiply 1.652891 by 5.
So 1.652891 × 5 ≈ 8.264455.
Problem 4
What will be the square root of (2 + 0.73)?
The square root is approximately 1.652891
Explanation
To find the square root, we need to find the sum of (2 + 0.73). 2 + 0.73 = 2.73, and then √2.73 ≈ 1.652891.
Therefore, the square root of (2 + 0.73) is approximately ±1.652891.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √2.73 units and the width ‘w’ is 3 units.
The perimeter of the rectangle is approximately 9.305782 units.
Explanation
Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√2.73 + 3) ≈ 2 × (1.652891 + 3) ≈ 2 × 4.652891 ≈ 9.305782 units.
FAQ on Square Root of 2.73
1.What is √2.73 in its simplest form?
2.Is 2.73 a perfect square?
3.What is the square of 2.73?
4.Is 2.73 a rational number?
5.What are the uses of square roots in real life?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 2.73?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 2.73?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 2.73
- Square root: A square root is the inverse of a square. For example, 4² = 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.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
- Long division method: A manual process for finding the square root of a number by dividing it into successive approximations.
- Approximation method: A method to estimate the value of a square root by finding two closer perfect squares around the number and using interpolation.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
