Square Root of 2.4
2026-02-28 13:57 Diff
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Last updated on August 5, 2025

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.

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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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √2.4?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √2.4 x 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (2.4 + 0.6)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √2.4 units and the width 'w' is 3.8 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 2.4

1.What is √2.4 in its simplest form?

The simplest form of √2.4 is expressed in decimal form as approximately 1.54919, as it cannot be simplified further using radical form.

2.Mention the factors of 2.4.

Factors of 2.4 in terms of whole numbers are 1, 2, 3, 4, 6, and 12 when considering 24 as it relates to 2.4 (by multiplying by 10).

3.Calculate the square of 2.4.

We get the square of 2.4 by multiplying the number by itself, that is 2.4 x 2.4 = 5.76.

4.Is 2.4 a prime number?

2.4 is not a prime number, as it is not a whole number and has more than two factors when considered as 24.

5.Is 2.4 divisible by?

2.4 is divisible by 1.2, 0.8, 0.6, and 0.4 when considering decimal divisors.

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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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.