Question

If two measured quantities are given as A = 3.0 m ± 0.3 m and B = 9.0 m ± 0.6 m, then the value of (AB)1/3 is

Answer 1

Answer:

(1) 3.0 m ± 0.9 m

(2) 27 m ± 0.9 m

(3) 3.0 m ± 0.2 m

(4) 9.0 m ± 0.1 m

Answer 2

Given : A = 3.0 m ± 0.3 m and B = 9.0 m ± 0.6 m

To Find :     $(AB)^{\frac{1}{3} }$

Solution:

$(AB)^{\frac{1}{3} }$   = ∛AB

A  = 3.0   ± 0.3

B = 9.0 m ± 0.6 m

∛AB  =  ∛( 3.0 * 9.0)  = 3.0

Δ∛AB  / AB  = (1/3) ( ΔA/A  + ΔB/B)

Δ∛AB  / 3  = (1/3) (  0.3/3.0 + 0.6/9.0)

Δ∛AB  / 3  = (1/3) (  0.1  + 0.067)

Δ∛AB =  0.167

3.0  ± 0.167

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