The Bakhshali Manuscript shows that another method for calculating nonperfect squares was being used in India by 400 CE. Use this method to find the approximate value of .


The nearest perfect square that is less than 22 is

, whose square root is

.

Add the square root from step 1 to to get 4.75.

Calculate the quantity one-half times the square of divided by the value found in step 2, or 4.75.


Subtract the value found in step 3 from the value found in step 2, or 4.75.

The approximate value of is

.