Square Root of 2024

The square root is the inverse of the square of the number. 2024 is a perfect square. The square root of 2024 is expressed in both radical and exponential form. In the radical form, it is expressed as √2024, whereas (2024)^(1/2) in the exponential form. √2024 = 44, which is a rational number because it can 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. This method helps in breaking down the number into its prime factors. 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 2024 is broken down into its prime factors.

Step 1: Finding the prime factors of 2024

Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7: 2^4 x 3^2 x 7^2

Step 2: Now we found the prime factors of 2024. Since 2024 is a perfect square, we can pair the prime factors as (2^2 x 3 x 7)^2 = (4 x 3 x 7)^2.

Step 3: Calculate the square root by taking one number from each pair, resulting in 4 x 3 x 7 = 84.

The long division method is used for non-perfect square numbers, but it can also be applied to perfect squares to verify results. Here’s how to find the square root using the long division method:

Step 1: Group the numbers from right to left. In the case of 2024, we group it as 20 and 24.

Step 2: Now find a number whose square is less than or equal to 20. We can say the number is 4 because 4 x 4 = 16. Subtract 16 from 20 to get a remainder of 4.

Step 3: Bring down 24, making the new dividend 424.

Step 4: Double the quotient to get the new divisor, 8. Find a number that fits as the next digit of the quotient multiplied by this divisor that is less than or equal to 424.

Step 5: The number is 4, as 84 x 4 = 336. Subtract 336 from 424 to get the remainder 88.

Step 6: Add a decimal point and bring down two zeros at a time. Repeat the division process to get more decimal places if needed.

However, since 2024 is a perfect square, the process stops here, confirming the square root as 44.

Approximation method is typically used for non-perfect squares but can be used for understanding. However, since 2024 is a perfect square, the approximation method would directly confirm the value.

Step 1: The closest perfect squares to 2024 are 1936 (44^2) and 2116 (46^2). Since 2024 is exactly between these, the square root is exactly 44.

Students do make mistakes while finding the square root, such as forgetting about the negative square root. Skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.

• 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.
   
• Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
   
• Perfect square: A number is a perfect square if it can be expressed as the square of an integer.
   
• Integers: The combination of whole numbers and negative numbers are integers, for example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, etc.
   
• 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.