100 LearnersLast updated on May 26th, 2025
Square Root of 45.14
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 such as vehicle design, finance, etc. Here, we will discuss the square root of 45.14.
What is the Square Root of 45.14?
The square root is the inverse of the square of a number. 45.14 is not a perfect square. The square root of 45.14 is expressed in both radical and exponential form.
In radical form, it is expressed as √45.14, whereas in exponential form as (45.14)^(1/2). √45.14 ≈ 6.718, 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 45.14
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 45.14 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we find 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 group the numbers from right to left. In the case of 45.14, we group it as 45 and 14.
Step 2: We need to find n whose square is less than or equal to 45. We can take n as 6 because 6 × 6 = 36, which is less than 45. Now, the quotient is 6, and after subtracting 36 from 45, the remainder is 9.
Step 3: Bring down 14, making the new dividend 914. Double the quotient and add a digit to it to form the new divisor.
Step 4: The new divisor, when multiplied by a digit, should give a product less than or equal to 914. Continuing with this process, we find that the square root of 45.14 is approximately 6.718.
Square Root of 45.14 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 45.14 using the approximation method.
Step 1: Find the closest perfect squares to 45.14. The nearest perfect squares are 36 and 49, as √36 = 6 and √49 = 7. So, √45.14 falls between 6 and 7.
Step 2: Applying the approximation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) = (45.14 - 36) / (49 - 36) = 9.14 / 13 ≈ 0.703
Using this formula, we add the decimal to the whole number approximation: 6 + 0.703 = 6.703.
Thus, the square root of 45.14 is approximately 6.703.
Common Mistakes and How to Avoid Them in the Square Root of 45.14
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division steps. Here are a few common mistakes:
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically use only the positive square root.
For example: √45.14 ≈ 6.718, but there is also -6.718.
Square Root of 45.14 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √45.14?
The area of the square is approximately 45.14 square units.
Explanation
The area of the square = side². The side length is given as √45.14. Area of the square = (√45.14)² = 45.14. Therefore, the area of the square box is approximately 45.14 square units.
Problem 2
A square-shaped building measuring 45.14 square feet is built; if each of the sides is √45.14, what will be the square feet of half of the building?
22.57 square feet
Explanation
The building is square-shaped, so divide the area by 2.
Dividing 45.14 by 2 gives 22.57.
So half of the building measures 22.57 square feet.
Problem 3
Calculate √45.14 × 5.
Approximately 33.59
Explanation
First, find the square root of 45.14, which is approximately 6.718.
Then multiply 6.718 by 5. 6.718 × 5 ≈ 33.59.
Problem 4
What will be the square root of (45 + 0.14)?
The square root is approximately 6.718
Explanation
Find the sum of (45 + 0.14), which is 45.14, and then take the square root.
The square root of 45.14 is approximately 6.718.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √45.14 units and the width ‘w’ is 10 units.
The perimeter of the rectangle is approximately 33.44 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√45.14 + 10) ≈ 2 × (6.718 + 10) = 2 × 16.718 ≈ 33.44 units.
FAQ on Square Root of 45.14
1.What is √45.14 in its simplest form?
2.Calculate the square of 45.14.
3.Is 45.14 a prime number?
4.What are the factors of 45.14?
5.45.14 is divisible by what integers?
Important Glossaries for the Square Root of 45.14
- Square root: The square root is the inverse operation of squaring a number. For example, if 5² = 25, then √25 = 5.
- Irrational number: A number that cannot be expressed as a fraction of two integers. For example, √2 is irrational.
- Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because 6 × 6 = 36.
- Long division method: A method used to find the square root of non-perfect square numbers by dividing and averaging.
- Approximation: Estimating a number close to its actual value. For example, √45.14 is approximately 6.718.
Explore More algebra
Previous to Square Root of 45.14
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.
