Multiply V 3 250 \sqrt[3]{3} . \sqrt[3]{ - 250} ​

Question

Multiply V 3 250

`\sqrt[3]{3} . \sqrt[3]{ - 250}`
​

Answer 1

Explanation:

we remember

(a×b)^c = a^c × b^c

and, of course, the other way around.

any root is also an exponent.

`\sqrt[c]{a} = {a}^{ (1)/(c) }`

and if c is an odd number, then a can be a negative number, making the result a negative number, as e.g. for c = 3

-a×-a×-a = -a³

so,

`\sqrt[3]{3} * \sqrt[3]{ - 250} = \sqrt[3]{3 * - 250} =`

`= \sqrt[3]{ - 750} = \sqrt[3]{ - 125 * 6} =`

`= \sqrt[3]{ - {5}^(3) * 6} = \sqrt[3]{ - {5}^(3) } * \sqrt[3]{6} =`

`= - 5 * \sqrt[3]{6} =`

= -9.085602964...