Question

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 .

Answer 1

The nearest perfect square that is less than 22 is 16, whose square root is 4. 

Add the square root from step 1 to 3/4 to get 4.75.

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) ÷ 4.75 = 0.06.

Subtract the value found in step 3 from the value found in step 2, or 4.75.
The approximate value of √22 is 4.69.

Answer 2

Answer:

1.  22

2. 4 

3. 0.06.

4.  4.69.

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