101 LearnersLast updated on May 26th, 2025
Square Root of 4.5
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 4.5.
What is the Square Root of 4.5?
The square root is the inverse of the square of the number. 4.5 is not a perfect square. The square root of 4.5 is expressed in both radical and exponential form. In the radical form, it is expressed as √4.5, whereas (4.5)^(1/2) in the exponential form. √4.5 = 2.12132, 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 4.5
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where 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 4.5 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. Since 4.5 is a single-digit number with a decimal, we can start directly.
Step 2: Find a number whose square is less than or equal to 4. The closest number is 2 since 2 × 2 = 4. The quotient is 2, and the remainder is 0.
Step 3: Bring down the next pair (50) to make it 050. Add the old divisor (2) with itself to get 4, which will be our new divisor.
Step 4: Find 4n such that 4n × n is less than or equal to 50. Let n be 1, so 41 × 1 = 41.
Step 5: Subtract 41 from 50 to get a remainder of 9.
Step 6: Since the dividend is less than the divisor, add a decimal point and bring down two zeros, making the new dividend 900.
Step 7: The new divisor is 42, so find 42n × n ≤ 900. Let n be 2. Then 422 × 2 = 844.
Step 8: Subtract 844 from 900 to get a remainder of 56.
Step 9: Continue the process until the desired decimal places are achieved. The quotient so far is 2.12.
The square root of 4.5 is approximately 2.12132.
Square Root of 4.5 by Approximation Method
The approximation method is another method for finding the 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 4.5 using the approximation method.
Step 1: Find the closest perfect squares around 4.5.
The closest perfect squares are 4 and 9. Therefore, √4.5 falls between √4 (which is 2) and √9 (which is 3).
Step 2: Use interpolation to estimate the square root of 4.5.
Using the formula: (4.5 - 4) / (9 - 4) = 0.1 Approximate square root: 2 + 0.1 * (3 - 2) = 2.1
Therefore, the approximate square root of 4.5 is 2.12132.
Common Mistakes and How to Avoid Them in the Square Root of 4.5
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that every positive number has both a positive and a negative square root. However, we usually consider only the positive square root unless specified otherwise.
For example, √4.5 = ±2.12132, but the principal square root is the positive one.
Square Root of 4.5 Examples
Problem 1
Can you help Lisa find the area of a square box if its side length is given as √4.5?
The area of the square is approximately 4.5 square units.
Explanation
The area of the square = side^2.
The side length is given as √4.5.
Area of the square = side^2 = (√4.5) × (√4.5) = 4.5.
Therefore, the area of the square box is 4.5 square units.
Problem 2
A square-shaped garden measures 4.5 square meters; if each of the sides is √4.5, what will be the square meters of half of the garden?
2.25 square meters
Explanation
Since the garden is square-shaped, dividing its area by 2 will give half the garden's area.
Dividing 4.5 by 2 = 2.25.
So, half of the garden measures 2.25 square meters.
Problem 3
Calculate √4.5 × 3.
6.364
Explanation
First, find the square root of 4.5, which is approximately 2.12132.
Then multiply 2.12132 by 3.
So, 2.12132 × 3 ≈ 6.364.
Problem 4
What will be the square root of (2 + 2.5)?
The square root is approximately 2.12132.
Explanation
To find the square root, we need to find the sum of (2 + 2.5), which equals 4.5.
The square root of 4.5 is approximately 2.12132.
Therefore, the square root of (2 + 2.5) is ±2.12132.
Problem 5
Find the perimeter of a square if its side length is √4.5 units.
The perimeter of the square is approximately 8.48528 units.
Explanation
The perimeter of a square = 4 × side. Perimeter = 4 × √4.5 ≈ 4 × 2.12132 ≈ 8.48528 units.
FAQ on Square Root of 4.5
1.What is √4.5 in its simplest form?
2.What are the factors of 4.5?
3.Calculate the square of 4.5.
4.Is 4.5 a rational number?
5.Is √4.5 a rational number?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 4.5?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 4.5?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 4.5
- 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 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.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is more commonly used due to its applications in the real world. This is known as the principal square root.
- Rational number: A rational number can be expressed as the ratio of two integers, with a non-zero denominator. Examples include 1/2, 3/4, and 5.
- Decimal: If a number has a whole number and a fractional part in a single expression, it is called a decimal. Examples include 7.86, 8.65, and 9.42.
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About BrightChamps in Saudi Arabia
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.
