Square Root of 2400
2026-02-28 01:08 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 squaring is finding the square root. The square root finds applications in fields like engineering, finance, etc. Here, we will discuss the square root of 2400.

What is the Square Root of 2400?

The square root is the inverse of squaring a number. 2400 is not a perfect square. The square root of 2400 is expressed in both radical and exponential form. In radical form, it is expressed as √2400, whereas (2400)^(1/2) in exponential form. √2400 ≈ 48.9898, which is an irrational number because it cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 2400

The prime factorization method is used for perfect square numbers. However, for non-perfect squares, methods like the long division method and approximation method are used. Let us now learn these methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 2400 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 2400 is broken down into its prime factors:

Step 1: Finding the prime factors of 2400 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 5 x 5: 2^4 x 3^1 x 5^2

Step 2: Now we found out the prime factors of 2400. The second step is to make pairs of those prime factors. Since 2400 is not a perfect square, the digits of the number can’t be grouped completely into pairs.

Therefore, calculating √2400 using prime factorization directly is not feasible.

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Square Root of 2400 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. In the case of 2400, we need to group it as 00 and 24.

Step 2: Now we need to find n whose square is less than or equal to 24. We can say n as '4' because 4 x 4 = 16, which is less than 24. Now, after subtracting 16 from 24, the remainder is 8.

Step 3: Bring down the next pair of digits, which is 00, to make the new dividend 800. Add the old divisor with the same number: 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor is 8n, and we need to find the value of n such that 8n x n ≤ 800. Let us consider n as 9; now, 89 x 9 = 801.

Step 5: Subtract 801 from 800 to get the result -1. Since we can't have a negative remainder, we adjust n to 8.

Step 6: Using a correct divisor, we find the remainder and continue the process to find a more accurate square root.

Step 7: After some iterations, we find the square root approximation. Continue these steps until we get two numbers after the decimal point.

So, the square root of √2400 ≈ 48.99.

Square Root of 2400 by Approximation Method

The approximation method is another way to find square roots. It's an easy method to estimate the square root of a given number. Now, let us learn how to find the square root of 2400 using the approximation method.

Step 1: We have to find the closest perfect square to √2400. The smallest perfect square less than 2400 is 2304 (48^2), and the largest perfect square more than 2400 is 2500 (50^2). √2400 falls between 48 and 50.

Step 2: Now we apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)

Using the formula: (2400 - 2304) ÷ (2500 - 2304) = 96 ÷ 196 ≈ 0.4898

Adding this to the smallest integer root, the approximation is 48 + 0.4898 ≈ 48.99.

Common Mistakes and How to Avoid Them in the Square Root of 2400

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let's look at a few common mistakes in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √240?

Okay, lets begin

The area of the square is 240 square units.

Explanation

The area of the square = side².

The side length is given as √240.

Area of the square = side² = √240 x √240 = 240.

Therefore, the area of the square box is 240 square units.

Well explained 👍

Problem 2

A square-shaped park measuring 2400 square meters is constructed; if each side is √2400 meters, what will be the area of half of the park?

Okay, lets begin

1200 square meters

Explanation

We divide the given area by 2, as the park is square-shaped.

Dividing 2400 by 2 = 1200.

So half of the park measures 1200 square meters.

Well explained 👍

Problem 3

Calculate √2400 x 5.

Okay, lets begin

Approximately 244.95

Explanation

The first step is to find the square root of 2400, which is approximately 48.99.

The second step is to multiply 48.99 by 5.

So, 48.99 x 5 ≈ 244.95.

Well explained 👍

Problem 4

What will be the square root of (2400 + 100)?

Okay, lets begin

The approximate square root is 50.

Explanation

To find the square root, we need to calculate the sum of (2400 + 100).

2400 + 100 = 2500, and then √2500 = 50.

Therefore, the square root of (2400 + 100) is ±50.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √2400 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is approximately 197.98 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√2400 + 50) = 2 × (48.99 + 50) ≈ 2 × 98.99 ≈ 197.98 units.

Well explained 👍

FAQ on Square Root of 2400

1.What is √2400 in its simplest form?

The prime factorization of 2400 is 2 x 2 x 2 x 2 x 3 x 5 x 5, so the simplest form of √2400 = √(2^4 x 3 x 5^2).

2.Mention the factors of 2400.

Factors of 2400 include 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 480, 600, 800, 1200, and 2400.

3.Calculate the square of 2400.

We get the square of 2400 by multiplying the number by itself, that is 2400 x 2400 = 5,760,000.

4.Is 2400 a prime number?

2400 is not a prime number, as it has more than two factors.

5.2400 is divisible by?

2400 has many factors; those include 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 480, 600, 800, 1200, and 2400.

Important Glossaries for the Square Root of 2400

  • Square root: A square root is the inverse operation of squaring a number. Example: 5^2 = 25, and the inverse of the square is the square root, that is √25 = 5.
  • 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 generally used due to its practical applications, which is known as the principal square root.
  • Prime factorization: Breaking down a number into a product of prime numbers. For example, the prime factorization of 2400 is 2^4 x 3^1 x 5^2.
  • Long division method: A method used to find the square root of non-perfect squares through a series of division steps to approximate the root.

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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.

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: He loves to play the quiz with kids through algebra to make kids love it.