167 LearnersLast updated on May 26th, 2025
Square Root of 20.25
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 various fields such as vehicle design and finance. Here, we will discuss the square root of 20.25.
What is the Square Root of 20.25?
The square root is the inverse of the square of the number. 20.25 is a perfect square. The square root of 20.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √20.25, whereas in exponential form it is (20.25)^(1/2). √20.25 = 4.5, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 20.25
The prime factorization method can be used for finding the square root of perfect square numbers. Other methods include long division and approximation methods. However, for 20.25, the square root can be directly calculated since it is a perfect square. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 20.25 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Below is how 20.25 is broken down into its prime factors:
Step 1: Express 20.25 as a fraction: 20.25 = 2025/100.
Step 2: Find the prime factors of 2025. Breaking it down, we get 3 x 3 x 3 x 3 x 5 x 5: 3^4 x 5^2.
Step 3: Since 2025 is a perfect square, its square root is the product of the square roots of its prime factors: (3^2 x 5)^2 = (3 x 5)^2 = 15^2.
Step 4: Since the square of 15 is 225, we know that the square root of 2025 is 45.
Therefore, the square root of 20.25 is 4.5.
Square Root of 20.25 by Long Division Method
The long division method is particularly used for non-perfect square numbers. However, for a number like 20.25 which is a perfect square, we can find the square root directly or verify using the long division method. Below is a simplified explanation:
Step 1: Start by expressing 20.25 as a decimal number.
Step 2: Group the numbers in pairs from the decimal point: 20, 25.
Step 3: Find a number whose square is less than or equal to the first group. For 20, the closest square is 16 (4^2). Place 4 as the first digit of the square root.
Step 4: Bring down the next pair (25), making it 425.
Step 5: The new divisor is twice the current quotient (4), so it is now 8. Find a digit x such that 8x x is less than or equal to 425. The digit is 5.
Step 6: Multiply 85 by 5 to get 425. Subtract 425 from 425 to get 0. The quotient is 4.5.
Thus, the square root of 20.25 is 4.5.
Square Root of 20.25 by Approximation Method
The approximation method is another method for finding square roots but is not necessary for perfect squares. However, it can be used for understanding:
Step 1: Find the closest perfect squares around 20.25. The closest are 16 (4^2) and 25 (5^2).
Step 2: Since 20.25 is directly between these values, the square root is between 4 and 5. Given its exact position, we can calculate it precisely as 4.5.
Therefore, the square root of 20.25 is approximately 4.5, which is exact due to it being a perfect square.
Common Mistakes and How to Avoid Them in the Square Root of 20.25
Students may make mistakes while finding the square root, including forgetting about the negative square root or improperly using methods. Let us look at a few of these mistakes in detail.
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 only the positive square root as it is the principal one.
For example: √25 = 5, but there is also -5 which should not be forgotten. For 20.25, the square root can be ±4.5.
Square root of 20.25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √20.25?
The area of the square is 20.25 square units.
Explanation
The area of the square = side^2.
The side length is given as √20.25.
Area of the square = side^2 = √20.25 x √20.25 = 4.5 × 4.5 = 20.25
Therefore, the area of the square box is 20.25 square units.
Problem 2
A square-shaped building measuring 20.25 square feet is built; if each of the sides is √20.25, what will be the square feet of half of the building?
10.125 square feet
Explanation
Since the building is square-shaped, dividing the given area by 2 gives us half of the building's area.
Dividing 20.25 by 2 gives us 10.125.
So half of the building measures 10.125 square feet.
Problem 3
Calculate √20.25 x 5.
22.5
Explanation
First, find the square root of 20.25, which is 4.5.
Then multiply 4.5 by 5. So, 4.5 x 5 = 22.5.
Problem 4
What will be the square root of (12.25 + 8)?
The square root is 4.5.
Explanation
To find the square root, calculate the sum of (12.25 + 8). 12.25 + 8 = 20.25, and then √20.25 = 4.5.
Therefore, the square root of (12.25 + 8) is ±4.5.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √20.25 units and the width ‘w’ is 10 units.
We find the perimeter of the rectangle as 29 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√20.25 + 10) = 2 × (4.5 + 10) = 2 × 14.5 = 29 units.
FAQ on Square Root of 20.25
1.What is √20.25 in its simplest form?
2.Mention the factors of 20.25.
3.Calculate the square of 20.25.
4.Is 20.25 a perfect square?
5.20.25 is divisible by?
Important Glossaries for the Square Root of 20.25
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not zero and p and q are integers.
- Perfect square: A perfect square is a number that has an integer as its square root. For example, 16 is a perfect square because its square root is 4.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
- Approximation: Approximation involves estimating the value of a number when precise calculation is not necessary.
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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.
