Square Root of 11600

The square root is the inverse of the square of the number. 11600 is not a perfect square. The square root of 11600 is expressed in both radical and exponential form. In the radical form, it is expressed as √11600, whereas (11600)^(1/2) in the exponential form. √11600 = 107.7033, which is an irrational number because it cannot 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. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are 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 11600 is broken down into its prime factors.

Step 1: Finding the prime factors of 11600

Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 29: 2^4 x 5^2 x 29

Step 2: Now we found out the prime factors of 11600. The second step is to make pairs of those prime factors. Since 11600 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 11600 using prime factorization is impossible.

The long division method is particularly used for 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 11600, we need to group it as 00 and 116.

Step 2: Now we need to find n whose square is less than or equal to 116. We can say n is 10 because 10 x 10 = 100, which is lesser than 116. The quotient is 10, and the remainder is 116 - 100 = 16.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 10 + 10 to get 20, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 20n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 20n x n ≤ 1600. Let us consider n as 8; now 208 x 8 = 1664, which is more than 1600, so n is 7.

Step 6: Subtract 1600 from 207 x 7 = 1449, the difference is 151, and the quotient is 107.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 15100.

Step 8: Now we need to find the new divisor, which is 215, because 215 x 7 = 1505.

Step 9: Subtracting 1505 from 15100, we get the result 595.

Step 10: Now the quotient is 107.7.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √11600 is 107.70

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. Now let us learn how to find the square root of 11600 using the approximation method.

Step 1: Now we have to find the closest perfect square of √11600. The smallest perfect square less than 11600 is 10000, and the largest perfect square greater than 11600 is 12100. √11600 falls somewhere between 100 and 110.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (11600 - 10000) ÷ (12100 - 10000) = 1600 / 2100 = 0.7619

Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 100 + 7.619 = 107.619, so the square root of 11600 is approximately 107.62.

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, that is, √16 = 4.

Irrational number: An irrational number is a number that cannot 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, 100 is a perfect square because it equals 10 x 10.

Long division method: A method used to find the square root of non-perfect squares by dividing the number into groups of digits and using a series of steps to approximate the square root.

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.