Square Root of 11016
2026-02-28 10:12 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-11016

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 11016, we need to group it as 16 and 110.

Step 2: Now we need to find n whose square is less than or equal to 110. We can say n as ‘10’ because 10^2 = 100 is lesser than or equal to 110. Now the quotient is 10 after subtracting 110 - 100, the remainder is 10.

Step 3: Now let us bring down 16, which is the new dividend. Add the old divisor with the same number: 10 + 10 = 20, which will be our new divisor.

Step 4: The new divisor will be 20n. We need to find the value of n that satisfies 20n × n ≤ 1016. Let us consider n as 5; now 205 × 5 = 1025.

Step 5: Subtract 1016 from 1025, the difference is -9. As it went negative, we take n as 4, now 204 × 4 = 816.

Step 6: Subtract 1016 from 816, the difference is 200, and the quotient becomes 104.

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 20000.

Step 8: Now we need to find the new divisor, which is 1049, because 1049 × 9 = 9441.

Step 9: Subtracting 9441 from 20000, we get the result 10559.

Step 10: Continue repeating these steps until we get two numbers after the decimal point or a suitable approximation.

So the square root of √11016 is approximately 104.941.