Sign Of The Cube Root Of A Negative Number

Asked By Chloe Chylly 20 points N/A Posted on - 10/30/2017

Today while solving a problem I got stuck while finding out the cube root of -125. What is the sign of a cube root of a negative number? Also, I am also curious whether the number will be a real number or not?

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Answered By Marcos P Blake 30 points N/A #305566

Sign Of The Cube Root Of A Negative Number

Although negative numbers cannot have real numbers as their square roots, they can have real cubic roots. An example of this is that the cubic root of -8 is -2. It has been verified that the cubic root of a negative number is always a negative number. It can be visualized from the fact that the product of two negative numbers is positive and thus the product of three same negative numbers will always be negative. Thus while finding out the cubic root of a negative number one just needs to find out the cubic root of the number without the negative sign, and then just add a negative sign before it. Various examples are shown in the picture below.

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• Posted on - 10/30/2017
• Question Category: Others