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?
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 :)
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)
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
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 :)
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......