102 LearnersLast updated on May 26th, 2025
Square Root of 45.53
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 45.53.
What is the Square Root of 45.53?
The square root is the inverse of the square of the number. 45.53 is not a perfect square. The square root of 45.53 is expressed in both radical and exponential form.
In the radical form, it is expressed as √45.53, whereas (45.53)^(1/2) in the exponential form. √45.53 ≈ 6.748, 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 45.53
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not suitable 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 45.53 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Since 45.53 is not a perfect square and not an integer, the prime factorization method is not applicable here. Calculating 45.53 using prime factorization is not possible.
Square Root of 45.53 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: Start by grouping the digits of 45.53 from left to right as 45 and 53.
Step 2: Find a number whose square is less than or equal to 45. The number is 6, because 6^2 = 36.
Step 3: Subtract 36 from 45 to get a remainder of 9. Bring down 53 to get the new dividend 953.
Step 4: Double the current quotient (6) to get 12, which will be the starting digits of the new divisor.
Step 5: Find a digit x such that 12x * x is less than or equal to 953. Try x = 7, because 127 * 7 = 889.
Step 6: Subtract 889 from 953 to get a remainder of 64.
Step 7: Add a decimal point and bring down two zeros to get 6400.
Step 8: The new divisor is 134. Find a digit x such that 134x * x is less than or equal to 6400. Try x = 4, because 1344 * 4 = 5376.
Step 9: Subtract 5376 from 6400 to get 1024.
Step 10: Continue the process until you reach the desired precision.
Thus, √45.53 ≈ 6.748.
Square Root of 45.53 by Approximation Method
The approximation method is another way to find 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 45.53 using the approximation method.
Step 1: Identify the closest perfect squares around 45.53. These are 36 and 49, with square roots 6 and 7, respectively.
Step 2: Use the formula: (Given number - Smallest perfect square) / (Greater perfect square - Smallest perfect square). (45.53 - 36) / (49 - 36) = 9.53 / 13 ≈ 0.733.
Step 3: Add this decimal to the smaller square root: 6 + 0.733 ≈ 6.733.
Thus, the square root of 45.53 is approximately 6.733.
Common Mistakes and How to Avoid Them in the Square Root of 45.53
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division method. Let us examine a few common 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, typically only the positive square root is considered for practical purposes.
For example: √50 ≈ ±7.07.
Square Root of 45.53 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √40?
The area of the square is 40 square units.
Explanation
The area of the square = side^2. The side length is given as √40.
Area of the square = side^2 = √40 × √40 = 40.
Therefore, the area of the square box is 40 square units.
Problem 2
A square-shaped garden measuring 45.53 square meters is built. If each side is √45.53, what will be the area of half of the garden?
22.765 square meters
Explanation
Divide the given area by 2 since the garden is square-shaped. 45.53 / 2 = 22.765.
So, half of the garden measures 22.765 square meters.
Problem 3
Calculate √45.53 × 3.
20.244
Explanation
First, find the square root of 45.53, which is approximately 6.748.
Then multiply 6.748 by 3. So, 6.748 × 3 ≈ 20.244.
Problem 4
What will be the square root of (40 + 5.53)?
The square root is approximately 6.748.
Explanation
To find the square root, first calculate the sum of (40 + 5.53). 40 + 5.53 = 45.53, and then √45.53 ≈ 6.748.
Therefore, the square root of (40 + 5.53) is approximately 6.748.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √40 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 73.437 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√40 + 20) ≈ 2 × (6.325 + 20) ≈ 2 × 26.325 ≈ 73.437 units.
FAQ on Square Root of 45.53
1.What is √45.53 in its simplest form?
2.Is 45.53 a perfect square?
3.Calculate the square of 45.53.
4.Is 45.53 a rational number?
5.What is the square root of 45.53 rounded to two decimal places?
Important Glossaries for the Square Root of 45.53
- Square root: A square root is the inverse of a square. For example, 4^2 = 16, and the inverse of the square is the square root, so √16 = 4.
- Irrational number: An irrational number cannot be written in the form of p/q, where q is not zero, and p and q are integers.
- Principal square root: A number has both positive and negative square roots, but the positive square root is more commonly used and is known as the principal square root.
- Long division method: A step-by-step approach to finding the square root of a non-perfect square number by dividing and averaging.
- Approximation method: A technique used to find the square root of a number by estimating between two known perfect squares and using proportional distances.
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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.
