Square Root of 2404
2026-02-28 23:58 Diff
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Last updated on August 5, 2025

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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 2404.

What is the Square Root of 2404?

The square root is the inverse of the square of the number. 2404 is not a perfect square. The square root of 2404 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2404, whereas in exponential form it is (2404)^(1/2). √2404 ≈ 49.034, 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 2404

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 and approximation methods are used. Let us now learn the following methods: 

  • Prime factorization method 
  • Long division method
  • Approximation method

Square Root of 2404 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 2404 is broken down into its prime factors.

Step 1: Finding the prime factors of 2404 Breaking it down, we get 2 × 2 × 601: 2² × 601

Step 2: Since 2404 is not a perfect square, we can't group the digits into pairs.

Therefore, calculating 2404 using prime factorization is impossible.

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Square Root of 2404 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 2404, we group it as 24 and 04.

Step 2: Now we need to find n whose square is less than or equal to 24. We can say n is 4 because 4 × 4 = 16, which is less than 24. The quotient is 4, and the remainder is 24 - 16 = 8.

Step 3: Bring down 04 to make the new dividend 804. Add the old divisor (4) with the same number, 4 + 4 = 8, which will be our new divisor's tens digit.

Step 4: We need to find a number n such that (80 + n) × n ≤ 804. Let n be 9, because 89 × 9 = 801.

Step 5: Subtract 801 from 804. The new remainder is 3.

Step 6: Since the remainder is less than the divisor, add a decimal point and two zeroes to the dividend. Now the new dividend is 300.

Step 7: The next divisor will be (89 × 10) + n, we need n such that (890 + n) × n ≤ 300, leading us to n as 0. Repeat these steps until the desired precision is achieved.

The quotient will approximate to √2404 = 49.034.

Square Root of 2404 by Approximation Method

The approximation method is another method for finding 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 2404 using the approximation method.

Step 1: Find the closest perfect squares around √2404. The smallest perfect square near 2404 is 2401, and the largest is 2500. √2404 falls between √2401 = 49 and √2500 = 50.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (2404 - 2401) / (2500 - 2401) = 3 / 99 ≈ 0.03

Add this to 49 to get the approximate square root: 49 + 0.03 = 49.03.

Common Mistakes and How to Avoid Them in the Square Root of 2404

Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. 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 √2404?

Okay, lets begin

The area of the square is approximately 5777.632 square units.

Explanation

The area of the square = side².

The side length is given as √2404.

Area of the square = side² = √2404 × √2404 ≈ 49.034 × 49.034 ≈ 5777.632

Therefore, the area of the square box is approximately 5777.632 square units.

Well explained 👍

Problem 2

A square-shaped garden measures 2404 square feet. If each side is √2404, what will be the square feet of half of the garden?

Okay, lets begin

1202 square feet

Explanation

We can just divide the given area by 2 since the garden is square-shaped.

Dividing 2404 by 2, we get 1202.

So half of the garden measures 1202 square feet.

Well explained 👍

Problem 3

Calculate √2404 × 5.

Okay, lets begin

Approximately 245.17

Explanation

First, find the square root of 2404, which is approximately 49.034.

Then multiply 49.034 by 5. 49.034 × 5 ≈ 245.17

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Problem 4

What will be the square root of (2400 + 4)?

Okay, lets begin

The square root is approximately 49.034

Explanation

To find the square root, we need to find the sum of (2400 + 4) 2400 + 4 = 2404, and then √2404 ≈ 49.034

Therefore, the square root of (2400 + 4) is approximately ±49.034

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √2404 units and the width ‘w’ is 40 units.

Okay, lets begin

Approximately 178.068 units

Explanation

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

Perimeter = 2 × (√2404 + 40) ≈ 2 × (49.034 + 40) ≈ 2 × 89.034 ≈ 178.068 units.

Well explained 👍

FAQ on Square Root of 2404

1.What is √2404 in its simplest form?

The prime factorization of 2404 is 2 × 2 × 601, so the simplest form of √2404 = √(2 × 2 × 601).

2.Mention the factors of 2404.

Factors of 2404 are 1, 2, 4, 601, 1202, and 2404.

3.Calculate the square of 2404.

We get the square of 2404 by multiplying the number by itself, which is 2404 × 2404 = 5777616.

4.Is 2404 a prime number?

2404 is not a prime number, as it has more than two factors.

5.2404 is divisible by?

2404 is divisible by the factors 1, 2, 4, 601, 1202, and 2404.

Important Glossaries for the Square Root of 2404

  • Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4.
  • Irrational number: An irrational number 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, but the positive square root is more commonly used and is known as the principal square root.
  • Prime factorization: The process of expressing a number as a product of its prime factors.
  • Long division method: A step-by-step approach used to find the square root of non-perfect squares.

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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.