Square Root of 2196

The square root is the inverse of the square of the number. 2196 is a perfect square. The square root of 2196 is expressed in both radical and exponential form. In the radical form, it is expressed as √2196, whereas (2196)^(1/2) in the exponential form. √2196 = 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 non-perfect square numbers, the long-division method and approximation method are used. Since 2196 is a perfect square, we can use the prime factorization method to find its square root.

The product of prime factors is the prime factorization of a number. Now let us look at how 2196 is broken down into its prime factors.

Step 1: Finding the prime factors of 2196. Breaking it down, we get 2 × 2 × 3 × 3 × 61: 2^2 × 3^2 × 61^1.

Step 2: Now we found out the prime factors of 2196. Since 2196 is a perfect square, we can take one number from each pair of prime factors and multiply them to get the square root.

Therefore, √2196 = 2 × 3 × √61 = 46.

The long division method is particularly used for non-perfect square numbers. However, it can also be used to verify perfect squares. 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 2196, we need to group it as 96 and 21.

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

Step 3: Now let us bring down 96, which is the new dividend. Add the old divisor with the same number 4 + 4 we get 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find the value of n such that 8n × n is less than or equal to 596. Considering n as 6, we have 86 × 6 = 516.

Step 5: Subtract 516 from 596; the difference is 80.

Step 6: Since the remainder is non-zero and less than the divisor, we stop here. The quotient is 46.

So, the square root of √2196 is 46.

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. However, since 2196 is a perfect square, the exact square root is 46, so an approximation method is not necessary here.

• Square root: A square root is the inverse of a square. Example: 46^2 = 2116, and the inverse of the square is the square root, that is, √2116 = 46.

• 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 that is the square of an integer. For example, 2196 is a perfect square because it is 46^2.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 2196 is 2^2 × 3^2 × 61.

• Dividend: A dividend is a number that is divided by another number. For example, in the division 2196 ÷ 2, 2196 is the dividend.