Why is -5 the answer of the cube root of negative 125 when the answer to the equivalent equation negative 125 to the power of 1/3 is not a real number?

Guest Jan 16, 2016

#3**+10 **

Why is -5 the answer of the cube root of negative 125 when the answer to the equivalent equation negative 125 to the power of 1/3 is not a real number?

All cube roots have 3 answers.

The calculator only looking for real roots only looks on the positive x axis.

No cubic root of -125 is on the positive x axis so a no real roots answer is returned. Some things calculators do not do very well. We have to interpret and understand the answers.

Here are the 3 roots of -125 displayed on a complex number plan.

I thought that you might find it interesting :)

Melody
Jan 17, 2016

#1**+4 **

It is REAL number just negative. Because -5 X -5=25 X -5=-125

If you state it like (-125i)^1/3=-5 (-1)^(5/6)

Guest Jan 16, 2016

#2**+5 **

If we assume the* real-value* root, the answer is -5 - a real number

If we assume the* principal* root the answer is 5*cube root (-1) - not a real number

CPhill
Jan 16, 2016

#3**+10 **

Best Answer

Why is -5 the answer of the cube root of negative 125 when the answer to the equivalent equation negative 125 to the power of 1/3 is not a real number?

All cube roots have 3 answers.

The calculator only looking for real roots only looks on the positive x axis.

No cubic root of -125 is on the positive x axis so a no real roots answer is returned. Some things calculators do not do very well. We have to interpret and understand the answers.

Here are the 3 roots of -125 displayed on a complex number plan.

I thought that you might find it interesting :)

Melody
Jan 17, 2016

#5**+5 **

Thanks Chris :)

You know, I do not really understand why calculators have such a tough time solving problems like this one.

It is not just one calc that has problems, it is almost universal......

Melody
Jan 17, 2016