Question

I’ll mark brainest! Find all the real cube roots of -0.000125

Answer 1

Answer:

-0.05

Step-by-step explanation:

This will become much easier if we can get the ugly decimal into a nice fraction form.

Start by recognising $\frac{1}{8}=0.125$. This is almost correct except the fraction is out by some number of factors of 10 (because the 125 part is correct but the number of 0s isn't).

$\frac{1}{80} = 0.0125\\\frac{1}{800}=0.00125\\\frac{1}{8000}=0.000125$

And hence we see that $-0.000125=-\frac{1}{8000}$ and now the cube root becomes easy to compute:

$\sqrt[3]{-0.000125} = \sqrt[3]{\frac{-1}{8000}} = \frac{\sqrt[3]{-1}}{\sqrt[3]{8000}} = \frac{-1}{20} = -0.05$.

Advanced: You ask for all real cube roots. however the function $y=\sqrt[3]{x}$ is described as bijective. This means for all x, there is only one y corresponding to it. (And also for all y there is only one x corresponding to that). This means there can only ever be one cube root of any real number.