Square root of non perfect square

Find the approximate value of square root of non perfect square.

Find square root of √ 54.

STEP 1 :

As we know 49 is nearest to the 54 that is perfact square root.

STEP 2 :

If 54 > 72 than we must add the values and first number of square root must be 7

STEP 3 :

Now 7 + ( 54 - 72 / 2 * 7)

= 7 + ( 54 - 49 / 14)

= 7 + (5 / 14)

= 7.3571428571429 Approx

So 7.3571428571429 is approx square root of 54 where as 7.3484692283495 is perfect square root.