Square Root of 12100

The square root is the inverse of the square of the number. 12100 is a perfect square. The square root of 12100 is expressed in both radical and exponential form. In the radical form, it is expressed as √12100, whereas (12100)^(1/2) in the exponential form. √12100 = 110, 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. 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 12100 is broken down into its prime factors.

Step 1: Finding the prime factors of 12100 Breaking it down, we get 2 x 2 x 5 x 5 x 11 x 11: 2² x 5² x 11²

Step 2: Now we found out the prime factors of 12100. The second step is to make pairs of those prime factors.

Since 12100 is a perfect square, the digits of the number can be grouped into pairs, allowing us to find the square root by taking one number from each pair. Therefore, √12100 = 2 x 5 x 11 = 110.

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 12100, we need to group it as 100 and 121.

Step 2: Now we need to find n whose square is 121. We can say n as '11' because 11 x 11 is equal to 121. Now the quotient is 11, and after subtracting 121 - 121, the remainder is 0.

Step 3: Now let us bring down 00. Add the old divisor's first digit with itself: 11 + 11 = 22, which will be our new divisor.

Step 4: The new divisor will be 220. Now, since the remainder was 0, we are done with the division. So the square root of √12100 is 110.

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 12100 using the approximation method.

Step 1: Now we have to find the closest perfect square of √12100. The closest perfect square to 12100 is 110², which is exactly 12100.

Therefore, the square root is precisely 110.

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes that students tend to make in detail.

• Square root: A square root is the inverse of a square. Example: 11² = 121, and the inverse of the square is the square root, which is √121 = 11.

• 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 can be expressed as the product of an integer with itself. Example: 12100 is a perfect square because it can be expressed as 110 x 110.

• Integers: The combination of whole numbers and negative numbers are integers. For example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7… are integers.

• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.