100 LearnersLast updated on May 26th, 2025
Square Root of 54.73
If a number is multiplied by the same number, the result is a square. The inverse of a square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 54.73.
What is the Square Root of 54.73?
The square root is the inverse of the square of a number. 54.73 is not a perfect square. The square root of 54.73 is expressed in both radical and exponential form.
In radical form, it is expressed as √54.73, whereas in exponential form it is (54.73)^(1/2). √54.73 ≈ 7.395, 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 54.73
The prime factorization method is used for perfect square numbers. However, for non-perfect squares like 54.73, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 54.73 by Long Division Method
The long division method is particularly used for non-perfect square numbers. 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 54.73, treat it as 5473 after multiplying by 100 (to work with whole numbers).
Step 2: Now, find a number whose square is less than or equal to 54. The number is 7 because 7 x 7 = 49. Subtract 49 from 54, leaving a remainder of 5.
Step 3: Bring down 73, making the new dividend 573. Double the quotient (7), to get 14, which becomes the new divisor.
Step 4: Find a digit 'x' such that 14x multiplied by x is less than or equal to 573. The digit is 4, since 144 x 4 = 576, which is greater than 573.
Step 5: Use 143 instead of 144. Thus, 143 x 4 = 572. Subtract 572 from 573, leaving a remainder of 1.
Step 6: Since the dividend is less than the divisor, add a decimal point and bring down two zeros, making it 100.
Step 7: Double 74 to get 148, and find a digit 'x' for 148x that results in a product less than or equal to 100. The digit is 0, since 1480 x 0 = 0.
Step 8: Continue this process to obtain the square root to the desired number of decimal places.
Thus, the square root of 54.73 is approximately 7.395.
Square Root of 54.73 by Approximation Method
The approximation method is another technique 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 54.73 using the approximation method.
Step 1: Identify the closest perfect squares around 54.73. The closest perfect squares are 49 and 64. Hence, √54.73 falls between 7 and 8.
Step 2: Use interpolation between these values.
Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (54.73 - 49) / (64 - 49) = 5.73 / 15 = 0.382
Step 3: Add this decimal to the smaller perfect square root: 7 + 0.382 ≈ 7.382.
Thus, by approximation, the square root of 54.73 is approximately 7.382.
Common Mistakes and How to Avoid Them in the Square Root of 54.73
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping the long division method. Below are some common mistakes and how to avoid them.
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 usually take the positive square root as it is the required one.
For example, √54.73 ≈ 7.395. There is also -7.395, which should not be forgotten.
Square Root of 54.73 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √54.73?
The area of the square is approximately 54.73 square units.
Explanation
The area of the square = side^2.
The side length is given as √54.73.
Area of the square = (√54.73) x (√54.73) = 54.73.
Therefore, the area of the square box is approximately 54.73 square units.
Problem 2
A square-shaped garden measures 54.73 square meters. If each of the sides is √54.73, what will be the square meters of half of the garden?
27.365 square meters
Explanation
Since the garden is square-shaped, dividing the given area by 2 gives the area of half the garden.
Dividing 54.73 by 2 = 27.365.
So, half of the garden measures 27.365 square meters.
Problem 3
Calculate √54.73 x 5.
36.975
Explanation
First, find the square root of 54.73, which is approximately 7.395.
Then, multiply 7.395 by 5.
So, 7.395 x 5 ≈ 36.975.
Problem 4
What will be the square root of (54.73 + 1)?
The square root is approximately 7.483.
Explanation
To find the square root, first compute the sum of (54.73 + 1). 54.73 + 1 = 55.73.
Then, √55.73 ≈ 7.483.
Therefore, the square root of (54.73 + 1) is approximately ±7.483.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √54.73 units and the width ‘w’ is 10 units.
The perimeter of the rectangle is approximately 34.79 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√54.73 + 10) = 2 × (7.395 + 10) = 2 × 17.395 = 34.79 units.
FAQ on Square Root of 54.73
1.What is √54.73 in its simplest form?
2.Is 54.73 a perfect square?
3.Calculate the square of 54.73.
4.Is 54.73 a rational number?
5.Can the square root of 54.73 be expressed as a fraction?
Important Glossaries for the Square Root of 54.73
- Square root: A square root is the inverse operation of squaring a number. For example, if 4^2 = 16, then √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction; its decimal form is non-repeating and non-terminating.
- Rational number: A rational number is a number that can be expressed as the quotient or fraction of two integers.
- Decimal: A decimal is a way of representing numbers that have a fractional part separated by a decimal point, such as 7.395.
- Interpolation: Interpolation is a method of estimating unknown values that fall between known values, often used in approximation techniques.
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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.
