100 LearnersLast updated on May 26th, 2025
Square Root of 53.21
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 53.21
What is the Square Root of 53.21?
The square root is the inverse of the square of the number. 53.21 is not a perfect square. The square root of 53.21 is expressed in both radical and exponential form.
In the radical form, it is expressed as √53.21, whereas (53.21)^(1/2) in the exponential form. √53.21 ≈ 7.296, 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 53.21
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 53.21 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Since 53.21 is not a whole number, prime factorization is not applicable.
Square Root of 53.21 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 group the numbers from right to left. In the case of 53.21, we treat it as 53 and 21.
Step 2: Now we need to find n whose square is less than or equal to 53. We can say n is 7 because 7 x 7 = 49, which is less than 53.
Step 3: Subtract 49 from 53, and the remainder is 4. Bring down the 21, making it 421.
Step 4: Double the quotient obtained in Step 2, which is 7, to get 14.
Step 5: Now, determine a digit x such that 14x * x ≤ 421. The value of x is 2, because 142 * 2 = 284.
Step 6: Subtract 284 from 421 to get a remainder of 137.
Step 7: Since the remainder is less than the divisor, add a decimal point and bring down two zeros, making it 13700.
Step 8: The new divisor is 144 (142 plus 2), and find x such that 144x * x ≤ 13700. After iterations, the value of x is found to be 9.
Step 9: Subtract and continue the process to find more decimal places as needed.
So the square root of √53.21 is approximately 7.296.
Square Root of 53.21 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 53.21 using the approximation method.
Step 1: Find the closest perfect squares around 53.21. The smallest perfect square is 49, and the largest perfect square is 64. √53.21 falls somewhere between 7 and 8.
Step 2: Now apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (53.21 - 49) / (64 - 49) = 4.21 / 15 = 0.2807. The approximation gives us 7 + 0.2807 ≈ 7.2807.
Thus, the square root of 53.21 is approximately 7.296.
Common Mistakes and How to Avoid Them in the Square Root of 53.21
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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 has both positive and negative square roots. However, we typically focus on the positive square root.
For example, √53.21 = 7.296, but there is also -7.296 which should not be forgotten.
Square Root of 53.21 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √53.21?
The area of the square is approximately 283.57 square units.
Explanation
The area of the square = side^2.
The side length is given as √53.21.
Area of the square = side^2 = √53.21 x √53.21 = 7.296 x 7.296 ≈ 53.21.
Therefore, the area of the square box is approximately 53.21 square units.
Problem 2
A square-shaped building measuring 53.21 square feet is built; if each of the sides is √53.21, what will be the square feet of half of the building?
Approximately 26.61 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 53.21 by 2 = 26.605.
So half of the building measures approximately 26.61 square feet.
Problem 3
Calculate √53.21 x 5.
Approximately 36.48.
Explanation
The first step is to find the square root of 53.21, which is approximately 7.296.
The second step is to multiply 7.296 with 5.
So, 7.296 x 5 ≈ 36.48.
Problem 4
What will be the square root of (53.21 + 6.79)?
The square root is approximately 8.
Explanation
To find the square root, we need to find the sum of (53.21 + 6.79). 53.21 + 6.79 = 60.
The square root of 60 is approximately 7.746.
Therefore, the square root of (53.21 + 6.79) is approximately ±7.746.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √53.21 units and the width ‘w’ is 10 units.
We find the perimeter of the rectangle as approximately 34.592 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√53.21 + 10) = 2 × (7.296 + 10) = 2 × 17.296 = 34.592 units.
FAQ on Square Root of 53.21
1.What is √53.21 in its simplest form?
2.Is 53.21 a perfect square?
3.Calculate the square of 53.21.
4.Is 53.21 a prime number?
5.What are some methods to find square roots?
Important Glossaries for the Square Root of 53.21
- Square root: A square root is the inverse of a square. Example: 3^2 = 9, and the inverse of the square is the square root, which is √9 = 3.
- 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.
- Approximation method: A technique used to find an estimated value of the square root of non-perfect squares.
- Long division method: A method used for finding the square root of a number by dividing it into groups and iterating through a series of steps to approximate the square root.
- Decimal: A number that consists of a whole number and a fractional part separated by a decimal point, such as 7.296.
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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.
