Question

\[-\sqrt[4]{81}\]

Answer 1

Well, what's the square root of 81?

Answer 2

\[-\sqrt[4]{81}\]

Answer 3

9

Answer 4

Right, and
\[ \sqrt[4]{81} = 81^{1/4} = (81^{1/2})^{1/2} = 9^{1/2} = .... \]

Answer 5

why dis 1/4 break down into 1/2?

Answer 6

because
\[ x^{ab} = (x^a)^b \] and \[ \frac{1}{4} = \frac{1}{2} . \frac{1}{2} \]

Answer 7

Hence
\[ x^{1/4} = x^{(1/2)(1/2)} = (x^{1/2})^{1/2} \]

Answer 8

& wouldn't it go to>>> \[\sqrt[2]{9}\] = 3

Answer 9

Yes. And that makes complete sense because \( 3^2 = 9 \) and hence \( 3^3 = 27 \) and hence \( 3^4 = 81 \).

Answer 10

\[-\sqrt[4]{81}=-\left(\sqrt[4]{81}\right)=-3 \]

Answer 11

so is the answer -3 or 3 ? & why?