Question

Simplify the problem thank you

Answer 1

-5

Explanation:

(-5)(-5)(-5)=-125

Answer 2

Given the expression:

`\displaystyle \large{ \sqrt[3]{ - 125} }`

Definition:

`\displaystyle \large{ y = \begin{cases} \pm \sqrt[n]{x} \longrightarrow n = (2,4,6,8,...) \: \: (x \geqslant 0) \\ \sqrt[n]{x}\longrightarrow n = (1,3,5,7,...) \: \: (x \in \R) \end{cases}}`

First, factor the -125. -125 comes from (-5)×(-5)×(-5) or (-5)^3.

`\displaystyle \large{ \sqrt[3]{ ( - 5) * ( - 5) * ( - 5)} }`

Because if (-5)^2 = 25 then 25×(-5) again will be -125.

Since this is the cube root, we have to pull out 3 terms in one. There are 3 fives that we can take off and therefore,

`\displaystyle \large \boxed{ - 5}`