The Bakhshali Manuscript shows that another method for calculating nonperfect squares was being used in India by 400 CE. Use thi
s 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 .
<span>The nearest perfect square that is less than 22 is 16, whose square root is 4.
</span><span>Add the square root from step 1 to 3/4 to get 4.75.
</span>Calculate the quantity one-half times the square of divided by the value found in step 2, or 4.75. (1/2 * (3/4)^2) <span>÷ 4.75 = 0.06. </span> Subtract the value found in step 3 from the value found in step 2, or 4.75. The approximate value of <span>√22 is 4.69.</span>
