Question

When we define nth root,
why is n<0 exlcuded?

For example,
why do we not define $\sqrt[-2]{x}$?

Answer 1

Answer:

  other notations work better

Step-by-step explanation:

You want to know why do we not define roots with negative indices:

  $\displaystyle \sqrt[{-2}]{x}$

Roots

The index in a surd represents the denominator of a fractional power:

  $\sqrt[n]{x}=x^\frac{1}{n}$

Using a negative number for a root index is the same as inverting the root:

  $\sqrt[-n]{x}=x^{-\frac{1}{n}}=\dfrac{1}{x^{\frac{1}{n}}}=\dfrac{1}{\sqrt[n]{x}}$

Essentially, there are more straightforward, less confusing and error-prone ways to write the same expression.

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Additional comment

Some calculators handle this easily. Others may not.

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