Answer:

To find the maximum possible percentage error in x we need to use the concept of error propagation. In this case we have the equation:

x = A√B

Let's calculate the maximum possible percentage error in x using the given percentage errors in A B and C.

The general formula for calculating percentage error in any expression involving multiplication division or powers is given by:

Percentage error = 100 * [(∆X / X) + (∆Y / Y) + (∆Z / Z) + ...]

Where ∆X ∆Y ∆Z represent the absolute errors in X Y Z respectively.

In this case the expressions A√B and C² both involve multiplication and powers so we can apply the formula.

Percentage error in A√B:

∆(A√B) = (∆A / A) + [(∆B / 2√B) * A]

= (∆A / A) + (∆B / 2√B) * A

Percentage error in C²:

∆(C²) = 2 (∆C / C)

Substituting the given errors:

∆(A√B) = (0.01)A + (0.02 / 2√B) * A

∆(C²) = 2 * (0.02)C = 0.04C

Now let's calculate the maximum possible percentage error in x by substituting the above errors in the formula:

Percentage error in x = 100 * [(∆(A√B) / (A√B)) + (∆(C²) / (C²))] = 100 * [((0.01)A + (0.02 / 2√B) * A) / (A√B) + 0.04C / (C²)]

Simplifying the expression further we get:

Percentage error in x = 100 * [(0.01 / √B) + (0.02 / (2B)] + 0.04 / C

Therefore the maximum possible percentage error in x is given by the above expression.