Question

evaluate cube root of -125

show steps / solution

Answer 1

\[\sqrt[3]{-125}\]

Answer 2

I'll give you a hint. \(-125 = -5^3\)

Answer 3

\[\sqrt[3]{-125}=\sqrt[3]{-1}*\sqrt[3]{125}\]

Answer 4

\[i*\sqrt[3]{125}= 5i\]

Answer 5

5i = -5

Answer 6

Uh.. The cubed root of -1 is not i.

Answer 7

yes

Answer 8

You're thinking of square roots. You can take the cubed root of a negative number.

Answer 9

\[\sqrt[3]{a^3} = a\]

Answer 10

Therefore:
\[\sqrt[3]{-125} = \sqrt[3]{-5^3} = ?\]

Answer 11

-5

Answer 12

Indeed.

Answer 13

so which is the correct solution then ?

Answer 14

\[5\sqrt[3]{-1?}\]

Answer 15

\[\sqrt[3]{-1}*\sqrt[3]{125}\]\[=5\sqrt[3]{-1}\]

Answer 16

The cubed root of -1 is -1. It's just -5 for the answer.

Answer 17

-1*5=-5