Square Root of 1196

The square root is the inverse of the square of the number. The number 1196 is a perfect square. The square root of 1196 is expressed in both radical and exponential form. In the radical form, it is expressed as √1196, whereas in the exponential form it is expressed as (1196)^(1/2). √1196 = 34, 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 such as long-division and approximation may be used. Let us now learn the following methods:

• Prime factorization method
• Long division method
• Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 1196 is broken down into its prime factors.

Step 1: Finding the prime factors of 1196. Breaking it down, we get 2 x 2 x 13 x 23 = 2² x 13 x 23.

Step 2: Now we found out the prime factors of 1196. The second step is to make pairs of those prime factors. Since 1196 is a perfect square, we can pair the factors as follows: (2×2) × (13) × (23).

Step 3: Take one factor from each pair and multiply them: 2 × 13 = 26.

Thus, the square root of 1196 using prime factorization is 34.

The long division method is particularly used 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 pairs of two. In the case of 1196, we can group it as 11 and 96.

Step 2: Now we need to find a number whose square is less than or equal to 11. We can say this number is 3 because 3 x 3 = 9, which is less than 11. Subtract 9 from 11 to get 2. Now, bring down the next pair (96), making the new dividend 296.

Step 3: Double the divisor (3) to get 6, and assume the new number is 6n. Find n such that 6n×n is less than or equal to 296. In this case, n is 4 because 64×4 = 256.

Step 4: Subtract 256 from 296 to get 40. Since we have no more pairs to bring down, we conclude the quotient as 34.

So the square root of √1196 is 34.

The approximation method can also be used to find the square roots, though it is more useful when dealing with non-perfect squares. Let's see how we find the square root of 1196 using this method.

Step 1: Identify the nearest perfect squares around 1196. The numbers 1156 (34²) and 1225 (35²) are perfect squares close to 1196.

Step 2: Since 1196 is already a perfect square and it falls exactly at 34, there's no need for approximation as the exact square root is 34.

• Square root: A square root is the inverse of a square. Example: 34² = 1156, and the inverse of the square is the square root, which is √1156 = 34.
   
• 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 perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6².
   
• Prime factorization: Prime factorization is the decomposition of a composite number into a product of its prime factors. Example: The prime factorization of 1196 is 2² x 13 x 23.
   
• Integer: Integers are the set of whole numbers and their opposites, including negative numbers, zero, and positive numbers. Examples include -3, 0, 1, and 5.