Square Root of 14884

The square root is the inverse of the square of the number. 14884 is a perfect square. The square root of 14884 is expressed in both radical and exponential form. In the radical form, it is expressed as √14884, whereas (14884)^(1/2) in the exponential form. √14884 = 122, 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, and since 14884 is a perfect square, this method can be used. However, long-division method and approximation method can also be applicable. Let us now 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 14884 is broken down into its prime factors.

Step 1: Finding the prime factors of 14884 Breaking it down, we get 2 x 2 x 37 x 37: 2² x 37²

Step 2: Now we found out the prime factors of 14884. The second step is to make pairs of those prime factors. Since we can make pairs of each factor, calculating 14884 using prime factorization is possible.

Step 3: The square root of 14884 is the product of one element from each pair: 2 x 37 = 74.

The long division method is particularly used for both perfect and 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 14884, we need to group it as 84 and 148.

Step 2: Now we need to find n whose square is less than or equal to 148. We can say n as ‘12’ because 12 x 12 = 144, which is less than or equal to 148. Now the quotient is 12, and the remainder is 4.

Step 3: Now let us bring down 84, which is the new dividend. Add the old divisor with the same number 12 + 12 to get 24, which will be our new divisor.

Step 4: The new divisor will be 24x. We need to find the value of x such that 24x x ≤ 484. Here, x = 2, since 242 x 2 = 484.

Step 5: Subtract 484 from 484. The remainder is 0, and the quotient is 122. So the square root of √14884 is 122.

The approximation method is another method for finding the 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 14884 using the approximation method.

Step 1: Now we have to find the closest perfect square of √14884. The closest perfect squares around 14884 are 14884 itself since it is a perfect square. √14884 = 122.

Step 2: Since 14884 is a perfect square, the approximation method directly gives us the result of 122.

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

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

• Perfect square: A perfect square is a number that is the square of an integer. Example: 144 is a perfect square because it is 12².

• Prime factorization: The process of breaking down a number into its prime factors. Example: Prime factorization of 14884 is 2 x 2 x 37 x 37.

• Long division method: A method used to find the square root of numbers, especially useful for both perfect and non-perfect squares, involving division-like steps.