103 LearnersLast updated on May 26th, 2025
Square Root of 5.3
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 various fields such as engineering, finance, etc. Here, we will discuss the square root of 5.3.
What is the Square Root of 5.3?
The square root is the inverse of the square of the number. 5.3 is not a perfect square. The square root of 5.3 is expressed in both radical and exponential form. In radical form, it is expressed as √5.3, whereas (5.3)^(1/2) in exponential form. √5.3 ≈ 2.3022, 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 5.3
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers, methods like the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 5.3 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we calculate the square root step-by-step to achieve a more accurate result.
Step 1: Begin by grouping the digits of the number from right to left. Since 5.3 is a decimal, we consider it as 5.3000.
Step 2: Find the largest number whose square is less than or equal to 5. The number is 2 because 2 × 2 = 4, which is less than 5. The quotient is 2, and the remainder is 1 (5 - 4).
Step 3: Bring down the next pair of digits, which are 30, to make the new dividend 130. Double the quotient (2), giving us 4, and write it below. Now, find a number n such that 4n × n is less than or equal to 130.
Step 4: The number n is 2, because 42 × 2 = 84, which is less than 130. Subtract 84 from 130 to get 46.
Step 5: Repeat the process by bringing down the next pair of zeros, making the dividend 4600. Double the current quotient (22) to get 44, then find a new n.
Step 6: Continuing this process gives us an approximate square root of 2.3022.
Square Root of 5.3 by Approximation Method
The approximation method is an easy way to find the square root of a given number by locating the closest perfect squares.
Step 1: Identify the closest perfect squares to 5.3.
The closest perfect square less than 5.3 is 4 (√4 = 2), and greater than 5.3 is 9 (√9 = 3). Therefore, √5.3 falls between 2 and 3.
Step 2: Using interpolation, we calculate: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (5.3 - 4) / (9 - 4) = 1.3 / 5 = 0.26
Step 3: Add the result of the interpolation to the square root of the smaller perfect square: 2 + 0.26 ≈ 2.26, which is a rough estimate.
Common Mistakes and How to Avoid Them in the Square Root of 5.3
Students often make mistakes while finding the square root, such as ignoring the negative square root or skipping steps in the long division method. Here 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 often focus on the positive square root, as it is usually the required value.
For example: √50 ≈ 7.07, but there is also -7.07.
Square root of 5.3 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5.3?
The area of the square is 5.3 square units.
Explanation
The area of the square = side².
The side length is given as √5.3.
Area of the square = side² = √5.3 × √5.3 = 5.3.
Therefore, the area of the square box is 5.3 square units.
Problem 2
A square-shaped park has an area of 5.3 square meters. If each of the sides is √5.3, what will be the square meters of half of the park?
2.65 square meters
Explanation
Since the park is square-shaped, divide the given area by 2 to find half: 5.3 / 2 = 2.65
So, half of the park measures 2.65 square meters.
Problem 3
Calculate √5.3 × 5.
11.511
Explanation
First, find the square root of 5.3, which is approximately 2.3022.
Multiply 2.3022 by 5: 2.3022 × 5 = 11.511
Problem 4
What will be the square root of (5.3 + 0.7)?
The square root is approximately 2.4495
Explanation
First, calculate the sum of 5.3 + 0.7: 5.3 + 0.7 = 6
Then, find the square root of 6: √6 ≈ 2.4495
Therefore, the square root of (5.3 + 0.7) is approximately ±2.4495.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √5.3 units and the width ‘w’ is 3 units.
The perimeter of the rectangle is approximately 10.6044 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√5.3 + 3) = 2 × (2.3022 + 3) ≈ 2 × 5.3022 ≈ 10.6044 units.
FAQ on Square Root of 5.3
1.What is √5.3 in its simplest form?
2.Is 5.3 a perfect square?
3.Can you express 5.3 as a fraction?
4.Is √5.3 an irrational number?
5.Can 5.3 be simplified further?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 5.3?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 5.3?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 5.3
- Square root: A square root is a value that, when multiplied by itself, gives the original number. For example, √16 = 4.
- Irrational number: An irrational number cannot be written as a simple fraction, meaning it cannot be expressed as p/q, where q ≠ 0, and p and q are integers.
- Decimal: A decimal is a number that includes a fraction represented with a point (e.g., 7.86, 8.65).
- Interpolation: A method used to estimate values within two known values in a sequence of values.
- Long Division: A method used to divide larger numbers that breaks down the division into a series of easier steps.
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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
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