Square Root of 11881

The square root is the inverse of the square of the number. 11881 is a perfect square. The square root of 11881 is expressed in both radical and exponential form. In the radical form, it is expressed as √11881, whereas (11881)^(1/2) in exponential form. √11881 = 109, 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 often used for perfect square numbers. However, the long division method and approximation method can also be 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 11881 is broken down into its prime factors.

Step 1: Finding the prime factors of 11881 Breaking it down, we get 11 x 11 x 11 x 11: 11⁴

Step 2: Now we found out the prime factors of 11881. The second step is to make pairs of those prime factors. Since 11881 is a perfect square, we can pair the prime factors. Each pair of 11 contributes a factor of 11 to the square root. Thus, √11881 = 11 x 11 = 109.

The long division method is helpful for both perfect and non-perfect square numbers. Here, we will 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 11881, we group it as 11, 88, and 1.

Step 2: Now we need to find n whose square is less than or equal to 11. We can say n is 3 because 3 x 3 = 9, which is less than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.

Step 3: Bring down the next pair, which is 88, making the new dividend 288. Add the old divisor with the same number, 3 + 3, to get 6, which will be part of our new divisor.

Step 4: The new divisor is 6n. We need to find n such that 6n x n is less than or equal to 288. We find n is 4 because 64 x 4 = 256, which is less than 288.

Step 5: Subtract 256 from 288; the difference is 32. The next digit in the quotient is 4.

Step 6: Bring down the next pair, which is 1, making the new dividend 321. Add the old divisor with the last digit of the quotient, 64 + 4, to get 68, which will be part of our new divisor.

Step 7: The new divisor is 68n. We need to find n such that 68n x n is less than or equal to 321. We find n is 1 because 681 x 1 = 681, which is greater than 321.

Hence, n is 0, and the process has reached a conclusion with the quotient being 109. So the square root of √11881 is 109.

The approximation method is another approach to finding square roots. It is a simple method to find the square root of a given number. Let us learn how to find the square root of 11881 using the approximation method.

Step 1: Find the closest perfect square numbers around 11881. The closest perfect square numbers are 10816 (104²) and 12100 (110²). √11881 falls between 108 and 110.

Step 2: Since 11881 is exactly 109², there is no need for further approximation. Therefore, the square root of 11881 is 109.

• Square root: A square root is the inverse of a square. Example: 11² = 121 and the inverse of the square is the square root that 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 is the square of an integer. Example: 121 is a perfect square because 11 x 11 = 121.

• Long division method: A method used for finding the square root of numbers by dividing and averaging.

• Prime factorization: The process of breaking down a number into its prime factors. Example: The prime factorization of 11881 is 11 x 11 x 11 x 11.