Square root of 160

Answer 1

12.649 (rounded)

Answer 2

sqrt(160)

We know that 12^2 = 144 and 13^2 = 169 .

So the square roots of 144 and 169 are 12 & 13 respectively,

Since 160 is between 144 & 169 , then its square root is between 12 & 13.

So by trial and Error , we try 12.5^2 = 156.25 This is too small so try 12.6

12.6^2 = 158.76 Still too smalle

12.7^2 = 161.29 This is too large , so try 12.68

12.68^2 = 160.7824 Still too large ,so try 12.67^2

12.67^2 = 16.5289 Too large

12.66^2 = 160.2756

12.65^2 = 160.0225

12.649^2 = 159.99

12.6495^2 = 160.0098503...

So to 4 d.p. the sqrt(160) ~ 12.6495

You can keep going like this, until you reach the required number of decimal places.

There is a 'mechanical' method to find square root, but it would take me all day to explain .

Per electronic calculator the answer is 12.64911064....