Square Root of 2116

The square root is the inverse of the square of the number. 2116 is a perfect square. The square root of 2116 is expressed in both radical and exponential form. In the radical form, it is expressed as √2116, whereas (2116)^(1/2) in the exponential form. √2116 = 46, 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 perfect squares like 2116, the prime factorization method is appropriate, but the long-division method can also be used. Let us now learn the following methods:

• Prime factorization method
• Long division method

The product of prime factors is the prime factorization of a number. Now let us look at how 2116 is broken down into its prime factors.

Step 1: Finding the prime factors of 2116

Breaking it down, we get 2 x 2 x 23 x 23: 2^2 x 23^2

Step 2: Now that we have found the prime factors of 2116, we make pairs of those prime factors. Since 2116 is a perfect square, the digits of the number can be grouped in pairs. Therefore, √2116 = 2 x 23 = 46.

The long division method is particularly useful for both perfect and non-perfect square numbers. 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 2116, we group it as 21 and 16.

Step 2: Now we need to find n whose square is less than or equal to 21. We can say n as ‘4’ because 4 x 4 = 16, which is less than 21. Now the quotient is 4, and after subtracting 16 from 21, the remainder is 5.

Step 3: Bring down 16, which is the new dividend. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor.

Step 4: The new divisor is 82. Now we need to find the value of n such that 8n x n ≤ 516. Let us consider n as 6, now 86 x 6 = 516.

Step 5: Subtracting 516 from 516 gives a remainder of 0, and the quotient is 46.

Step 6: Since we reached a remainder of 0, the square root of 2116 is 46.

Since 2116 is a perfect square, the approximation method isn't necessary here. However, for non-perfect squares, the approximation method helps find the square root.

Here, we simply verify that 46 x 46 = 2116, confirming the square root.

• Square root: A square root is the inverse of a square. For example: 4^2 = 16, and the inverse of the square is the square root, i.e., √16 = 4.
   
• Rational number: A rational number 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 perfect square is a number that is the square of an integer, for example, 16, 36, 49, etc.
   
• Integer: Integers are the combination of whole numbers and negative numbers, for example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, etc.
   
• Divisor: A divisor is a number by which another number is divided without leaving a remainder. For example, 2 is a divisor of 8.