Square Root of 14400

The square root is the inverse of the square of the number. 14400 is a perfect square. The square root of 14400 is expressed in both radical and exponential forms. In the radical form, it is expressed as √14400, whereas 14400^(1/2) in the exponential form. √14400 = 120, 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. Since 14400 is a perfect square, we can use the prime factorization method. Let us learn the following methods:

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 14400 is broken down into its prime factors.

Step 1: Finding the prime factors of 14400 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 5: 2⁴ x 3² x 5⁴

Step 2: Now we found out the prime factors of 14400. The next step is to make pairs of those prime factors. Since 14400 is a perfect square, we can group the digits in pairs. Therefore, √14400 = (2² x 3 x 5²) = 120.

The long division method is particularly used for 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 14400, we need to group the numbers as 400 and 144.

Step 2: Now we need to find n whose square is less than or equal to 144. We can say n is 12 because 12 x 12 = 144. Now the quotient is 12 after subtracting 144 - 144, the remainder is 0.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 12 + 12, we get 24, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 240 as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 240 x n ≤ 00. Since the dividend is zero, the process stops here. So the square root of √14400 is 120.

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 14400 using the approximation method.

Step 1: Now we have to find the closest perfect square of √14400. The smallest perfect square of 14400 is 14400 itself, so the square root is exactly 120.

• 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.

• Perfect square: A perfect square is a number that has an integer as its square root, such as 14400, which is 120²

• Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.

• Long division method: A method used to find the square root of a number by dividing the number into groups starting from the right.

• Prime factorization: The process of expressing a number as a product of its prime factors.