When you are finding the square root of a number that does not have a perfect square you find out the closest perfect square roots to the number, which in this case is 64 and 81.

64—76—81              64=8×8         76=?x?       81=9×9

Then you find out half way between 8 and 9 which would be 8.5.

-An easy way to find out the estimation of 76 is to add 64 and 8.5.

64+8.5=72.5

After that, you know that 64 x 8.5 is lower than 76, so you know that it should be higher.

Next you can try 5.6 which is still to low, so if you try 5.7 it should be right.