Answer :
The square root of 176. So, √176 = 13.266.
To find the square root of 176, let's use the long division method:
Start by grouping the digits in pairs from right to left: 1|76.
Find the largest perfect square less than or equal to 1. The largest perfect square less than 1 is 0, so our quotient is 0 and the remainder is 1|76.
Bring down the next pair of digits, 76. Now we have 176.
Double the quotient (0) and write it as the divisor. 0 x 20 = 0, so we have 0|00.
Find the largest digit 'x' to append to 0 so that x * (x + 20) ≤ 176. The largest digit is 8, so we try 08 as our new divisor. 80 * 80 = 6400, which is too large. Let's try 70. 70 * 70 = 4900, which is good. So, we put 7 in the quotient. Our new dividend is 176 - 4900 = 286.
Double the quotient (7) and append it to the divisor: 140. Find the largest digit 'x' such that x * (x + 140) ≤ 286. The largest digit is 1, so we try 141 as our new divisor. 141 * 1 = 141, subtracting this from 286 gives 145.
Double the quotient (71) and append it to the divisor: 1420. Find the largest digit 'x' such that x * (x + 1420) ≤ 14500. The largest digit is 0, so we try 14200 as our new divisor. 14200 * 0 = 0, subtracting this from 14500 gives 14500.
Since the remainder is 0, we have found the square root of 176. So, √176 = 13.266.
