Question

cube root of -512/343









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Answer 1

Are you allowed to use a calculator?

Answer 2

He typed "cube root," @mayankdevnani ! :)

Answer 3

\[\huge \sqrt[3]{\frac{-512}{343}}\] I modified what you typed :)

Answer 4

\[\sqrt[3]{\frac{-512}{343}} =\sqrt[3]{\frac{-512}{343}} \]
\[\sqrt[3]{\frac{(-8) \times (-8) \times (-8)}{(7)\times(7)\times(7)}} = \frac{-8}{7}\]

Answer 5

Note that the following expression can be re-written as:\[\large \bf \sqrt[3]{\frac{ (-2^3)^3 }{ 7^3 }}=\frac{ \sqrt[3]{(-2^3)^3} }{ \sqrt[3]{7^3} }=??\]

Answer 6

It's tough at first, but very pretty, huh?

Answer 7

It looks like you have the solution before you, @vishwasdevnani . If you haven't memorized your cubes, you'd just want to guess, and then see how close you are. Like, if you guessed \(\sqrt[3]{(-9)^3}\) for the numerator, you see that you had \(\sqrt[3]{-729}\), which is greater than \(\sqrt[3]{-512}\) and so you'd have to guess a smaller number, like \(\sqrt[3]{(-8)^3}\), which is the numerator.

Answer 8

-8/7