What is the simplified value of \(\dfrac{(0.05)^3 + (0.005)^3}{(0.25)^3 + (0.025)^3}\)?
0.008
Notice that 0.05 = 0.25 / 5 and 0.005 = 0.025 / 5. So the numerator is \(\dfrac{1}{5^3}\) times the denominator.
Factor out the common factor:
\((0.05)^3 + (0.005)^3 = \left(\dfrac{0.25}{5}\right)^3 + \left(\dfrac{0.025}{5}\right)^3 = \dfrac{(0.25)^3}{125} + \dfrac{(0.025)^3}{125} = \dfrac{(0.25)^3 + (0.025)^3}{125}\)
Therefore:
\(\dfrac{(0.05)^3 + (0.005)^3}{(0.25)^3 + (0.025)^3} = \dfrac{1}{125} = 0.008\)
Hence the simplified value is 0.008.
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Important Questions from Cubes & Cube Roots
If \(x=3-3^{1/3}-3^{2/3}\), then what is \(x(x-3)(x-6)\) equal to?
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