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.

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

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.

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.

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.

• 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.