Whats the product of 6/9 and 3/8 in simplest form

Mathematics

1 answer:

vaieri [72.5K]3 years ago

3 0

The answer is (1/4)
work:

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

Ymorist [56]

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 <em>all </em>real cube roots. however the function $y=\sqrt[3]{x}$ is described as <em>bijective</em>. 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.