Square Root of 24336

The square root is the inverse of the square of the number. 24336 is a perfect square. The square root of 24336 is expressed in both radical and exponential form. In the radical form, it is expressed as √24336, whereas (24336)^(1/2) in the exponential form. √24336 = 156, 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. For non-perfect square numbers, methods like the long-division method and approximation method are used. Here, we will use the prime factorization method since 24336 is a perfect square.

The product of prime factors is the prime factorization of a number. Now, let us look at how 24336 is broken down into its prime factors.

Step 1: Finding the prime factors of 24336 Breaking it down, we get 2 × 2 × 2 × 2 × 3 × 3 × 13 × 13: 2⁴ × 3² × 13²

Step 2: Now we found the prime factors of 24336. The second step is to make pairs of those prime factors. Since 24336 is a perfect square, we can perfectly group the digits into pairs: (2 × 2) × (2 × 2) × (3) × (3) × (13) × (13)

Step 3: Taking one number from each pair gives us the square root of 24336. Thus, √24336 = 2 × 2 × 3 × 13 = 156.

The long division method is a systematic approach to finding the square root of non-perfect squares, but it can also be used for perfect squares. Here’s how you can find the square root using the long division method.

Step 1: Start by grouping the digits of 24336 from right to left in pairs: 24|336

Step 2: Find a number whose square is less than or equal to 24. The number is 4 because 4 × 4 = 16, and the remainder is 8.

Step 3: Bring down the next pair of digits, making the new dividend 8336. Double the quotient (which is 4) and write it as 8, leaving space for the next digit of the new divisor 8_.

Step 4: Find a digit to fill the blank in 8_ such that 8_n × n is less than or equal to 8336. The digit is 3, giving 83 × 3 = 249, and the remainder is 0.

Step 5: Repeat the process if necessary. Here, the square root of 24336 is 156 exactly, with no remainder.

Approximation is generally used for non-perfect squares. However, knowing the approximation method is useful.

Step 1: Identify the perfect squares closest to 24336. The perfect square closest to 24336 is exactly 24336 since it is a perfect square.

Step 2: Since 24336 is already a perfect square, we find that √24336 = 156 directly.

• Square root: A square root is the inverse of a square. Example: 12² = 144 and the inverse of the square is the square root, which is √144 = 12.

• Perfect square: A perfect square is a number that is the square of an integer. For example, 4, 9, 16, 25, etc., are perfect squares.

• 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.

• Exponent: An exponent refers to the number of times a number is multiplied by itself. For example, in 2³, 3 is the exponent, indicating 2 × 2 × 2.

• Divisor: A divisor is a number by which another number is to be divided. For example, in 12 ÷ 3 = 4, 3 is the divisor.