103 LearnersLast updated on May 26th, 2025
Square Root of 4.8
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 4.8.
What is the Square Root of 4.8?
The square root is the inverse of squaring a number. Since 4.8 is not a perfect square, its square root is expressed in both radical and exponential form. In radical form, it is expressed as √4.8, whereas in exponential form it is (4.8)^(1/2). √4.8 ≈ 2.19089, which is an irrational number because it cannot be expressed as a simple fraction.
Finding the Square Root of 4.8
For non-perfect square numbers, methods like the long division method and approximation method are used since the prime factorization method is not applicable. Let us now learn these methods:
- Long division method
- Approximation method
Square Root of 4.8 by Long Division Method
The long division method is useful for finding square roots of non-perfect square numbers. Here is how to find the square root of 4.8 using this method, step by step:
Step 1: First, we need to group the numbers from right to left. Since 4.8 is a single-digit decimal, we consider 4.8 as 48 with a decimal point later.
Step 2: Find a number (n) whose square is less than or equal to 4. We choose n as 2 because 2^2 = 4.
Step 3: Subtract 4 from 4, resulting in 0. Bring down 80, making the new dividend 80.
Step 4: Double the current quotient (2) to get 4, which will be the start of the new divisor.
Step 5: Find a digit (x) such that 4x * x is less than or equal to 80. Choose x as 2, because 42 * 2 = 84 is too large.
Step 6: Use 41 * 1 = 41. Subtract 41 from 80, resulting in 39.
Step 7: Since 39 is smaller than 41, we add a decimal point and bring down two zeroes, making the new dividend 3900.
Step 8: Double the current quotient (21) to get 42, which will be the first part of the new divisor.
Step 9: Find a digit (y) such that 42y * y is less than or equal to 3900. Choose y as 9, because 429 * 9 = 3861 is less than 3900.
Step 10: Subtract 3861 from 3900, resulting in 39. The quotient is 2.19.
The approximate value of √4.8 is 2.19.
Square Root of 4.8 by Approximation Method
The approximation method is a simpler way to find square roots. Here is how to find the square root of 4.8 using this method:
Step 1: Identify the closest perfect squares to 4.8.
The closest perfect squares are 4 (2^2) and 9 (3^2). Thus, √4.8 is between 2 and 3.
Step 2: Use linear interpolation to estimate the square root: (4.8 - 4) / (9 - 4) = 0.8 / 5 = 0.16 Add this to the lower bound: 2 + 0.16 = 2.16
Therefore, √4.8 is approximately 2.16.
Common Mistakes and How to Avoid Them in the Square Root of 4.8
Students often make errors when finding square roots, such as forgetting about the negative square root, or misapplying methods. Here are some common mistakes to watch out for:
Mistake 1
Forgetting about the negative square root
Numbers have both positive and negative square roots, though typically only the positive is considered in practical scenarios.
For example, √4.8 ≈ 2.19, but there is also -2.19.
Square Root of 4.8 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4.8?
The area of the square is approximately 4.8 square units.
Explanation
The area of the square = side^2.
The side length is given as √4.8.
Area of the square = (√4.8)^2 = 4.8.
Therefore, the area of the square box is approximately 4.8 square units.
Problem 2
A square-shaped garden measures 4.8 square meters; if each side is √4.8 meters, what is the area of half the garden?
2.4 square meters
Explanation
To find half the area of the garden, divide the total area by 2.
Dividing 4.8 by 2 gives 2.4.
Thus, half of the garden measures 2.4 square meters.
Problem 3
Calculate √4.8 × 5.
Approximately 10.95
Explanation
First, find the square root of 4.8, which is approximately 2.19.
Then, multiply 2.19 by 5.
So, 2.19 × 5 ≈ 10.95.
Problem 4
What will be the square root of (4 + 0.8)?
The square root is approximately 2.19.
Explanation
To find the square root, first find the sum of (4 + 0.8), which is 4.8.
Then find √4.8, which is approximately 2.19.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √4.8 units and the width 'w' is 4 units.
The perimeter of the rectangle is approximately 12.38 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4.8 + 4) ≈ 2 × (2.19 + 4) = 2 × 6.19 ≈ 12.38 units.
FAQ on Square Root of 4.8
1.What is √4.8 in its simplest form?
2.Calculate the square of 4.8.
3.Is 4.8 a perfect square?
4.Is the square root of 4.8 rational?
5.How can 4.8 be expressed as a fraction?
Important Glossaries for the Square Root of 4.8
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √9 = 3.
- Irrational number: A number that cannot be written as a simple fraction (p/q where q ≠ 0) is called an irrational number. √4.8 is an example.
- Radical: A radical is an expression that includes a root, such as a square root or cube root. Example: √4.8.
- Decimal: A decimal is a number that consists of a whole number and a fractional part, separated by a decimal point. Example: 4.8.
- Approximation: The process of finding a value that is close to the exact answer, often used with irrational numbers. Example: √4.8 ≈ 2.19.
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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.
