Square Root of 17.7
2026-02-28 01:34 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-17.7

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 17.7, treat it as 1770 by considering it in the hundredths place.

Step 2: Now we need to find n whose square is less than or equal to 1. We can say n is '1' because 1 × 1 is less than or equal to 1. Now the quotient is 1, and after subtracting 1 - 1, the remainder is 0.

Step 3: Now let us bring down 77, making the new dividend 170. Add the old divisor with the same number 1 + 1, we get 2, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 170. Let us consider n as 8; now 28 × 8 = 224, which exceeds 170. Try n as 6; 26 × 6 = 156, which fits.

Step 6: Subtract 156 from 170; the difference is 14, and the quotient is 16.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down two zeroes, making the new dividend 1400.

Step 8: Now, the new divisor is 32 because 326 × 4 = 1304.

Step 9: Subtracting 1304 from 1400 results in 96.

Step 10: Now the quotient is 4.2.

Step 11: Continue doing these steps until you have two numbers after the decimal point or the remainder is zero.

So, the square root of √17.7 is approximately 4.21.