104 LearnersLast updated on May 26th, 2025
Square Root of 2.4
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 2.4.
What is the Square Root of 2.4?
The square root is the inverse of the square of the number. 2.4 is not a perfect square. The square root of 2.4 is expressed in both radical and exponential form. In the radical form, it is expressed as √2.4, whereas (2.4)^(1/2) in the exponential form. √2.4 ≈ 1.54919, 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 2.4
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 2.4 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2.4 is broken down into its prime factors.
Step 1: Multiply 2.4 by 10 to get a whole number, resulting in 24.
Step 2: Finding the prime factors of 24. Breaking it down, we get 2 x 2 x 2 x 3: 2^3 x 3^1
Step 3: Now, take the square root of 24 and divide it by the square root of 10 to get the square root of 2.4.
Step 4: Since 24 is not a perfect square, the digits cannot be grouped in pairs.
Therefore, calculating 2.4 using prime factorization directly is not straightforward.
Square Root of 2.4 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 multiply 2.4 by 100 to work with whole numbers, resulting in 240.
Step 2: Group the numbers from right to left. In the case of 240, we need to group it as 40 and 2.
Step 3: Find n whose square is less than or equal to 2. We can say n is '1' because 1 x 1 is less than or equal to 2. The quotient is 1, and the remainder is 1.
Step 4: Bring down the next group which is 40, making the new dividend 140. Double the previous quotient (1), which gives us 2 as the new divisor.
Step 5: Find a digit, say 'm', such that 2m x m is less than or equal to 140. Here, m is 5 because 25 x 5 = 125.
Step 6: Subtract 125 from 140; the difference is 15. Bring down two zeros to get 1500.
Step 7: The new divisor is 30 (2 * 5) plus the next digit from the quotient. Continue these steps until you achieve the desired precision.
Thus, the square root of 2.4 is approximately 1.549.
Square Root of 2.4 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 2.4 using the approximation method.
Step 1: Find the closest perfect squares around 2.4. The smallest perfect square is 1 (√1 = 1) and the largest perfect square is 4 (√4 = 2). Thus, √2.4 falls between 1 and 2.
Step 2: Now, apply the formula: (Given number - smallest perfect square) / (greater perfect square - smallest perfect square) (2.4 - 1) / (4 - 1) = 1.4 / 3 ≈ 0.467
Step 3: Add this value to the square root of the smaller perfect square: 1 + 0.467 = 1.467 Thus, the square root of 2.4 is approximately 1.549 when calculated more precisely.
Common Mistakes and How to Avoid Them in the Square Root of 2.4
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods, etc. 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 does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07; there is also -7.07, which should not be forgotten.
Square root of 2.4 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2.4?
The area of the square is approximately 2.4 square units.
Explanation
The area of the square = side².
The side length is given as √2.4.
Area of the square = (√2.4)² = 2.4.
Therefore, the area of the square box is approximately 2.4 square units.
Problem 2
A square-shaped building measuring 2.4 square feet is built; if each of the sides is √2.4, what will be the square feet of half of the building?
1.2 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2.4 by 2 = we get 1.2.
So half of the building measures 1.2 square feet.
Problem 3
Calculate √2.4 x 5.
Approximately 7.74595
Explanation
The first step is to find the square root of 2.4, which is approximately 1.54919.
The second step is to multiply 1.54919 by 5.
So 1.54919 x 5 ≈ 7.74595.
Problem 4
What will be the square root of (2.4 + 0.6)?
The square root is approximately 1.73205.
Explanation
To find the square root, we need to find the sum of (2.4 + 0.6). 2.4 + 0.6 = 3, and then √3 ≈ 1.73205.
Therefore, the square root of (2.4 + 0.6) is approximately ±1.73205.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √2.4 units and the width 'w' is 3.8 units.
We find the perimeter of the rectangle as approximately 10.69838 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2.4 + 3.8)
≈ 2 × (1.54919 + 3.8)
≈ 2 × 5.34919
≈ 10.69838 units.
FAQ on Square Root of 2.4
1.What is √2.4 in its simplest form?
2.Mention the factors of 2.4.
3.Calculate the square of 2.4.
4.Is 2.4 a prime number?
5.Is 2.4 divisible by?
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 2.4?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 2.4?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 2.4
- 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.
- 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.
- 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.
- Long division method: A mathematical method used to find the square root of non-perfect squares through a series of steps involving division and averaging.
- Approximation method: A technique used to find an approximate value of a square root by identifying nearby perfect squares and interpolating between them.
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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.
