Square Root of 1616
2026-02-28 00:56 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1616

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: Begin by grouping the numbers from right to left. In the case of 1616, group it as 16 and 16.

Step 2: Find n whose square is less than or equal to 16. Here, n is 4 because 4^2 = 16. Now the quotient is 4 after subtracting 16-16, the remainder is 0.

Step 3: Bring down the next pair of digits, which is 16. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor.

Step 4: The new divisor will be 8n, where we need to find the value of n.

Step 5: Find 8n × n ≤ 16. Let us consider n as 2, now 8 x 2 x 2 = 32

Step 6: Subtract 16 from 32; since 32 is greater, choose n such that the multiplication is less than or equal to the dividend. The closest possible n is 0.

Step 7: Since the dividend is less than the divisor, add a decimal point. This allows us to add two zeroes to the dividend. Now the new dividend is 1600.

Step 8: Find the new divisor, which is 80n, where n is 2 because 802 ✖ 2 = 1600.

Step 9: Subtract 1600 from 1600; the result is 0.

Step 10: Now the quotient is 40.2

Step 11: Continue these steps until there are two decimal places in the quotient or the remainder is zero.

So the square root of √1616 is approximately 40.20.