Question

Geometric mean of 11 and 1331?

Answer 1

\[\sqrt{11*1331}\]
Geometric mean of 2 numbers is the square root of their product

Answer 2

Our teacher wants us to put it in radical form. So would that mean that I would just put the product (121) into radical form?

Answer 3

Just leave the answer as 121. Your teachers point was to write a precise expression for it. For example, the geometric mean of 2 and 4 is
\[ \sqrt{8} = 2\sqrt{2} \]
this is radical form, and doesn't involve any messy, imprecise decimal expansions.

Answer 4

*teacher's

Answer 5

121 can be reduced to 11 though. So should I leave my answer as 11?

Answer 6

No, it can't here because the answer is NOT
\[ \sqrt{121} \]

Answer 7

Ohh, okay. Thank you.

Answer 8

\[ \sqrt{11 \cdot 1331} = \sqrt{11 \cdot 11^3} = \sqrt{11^4} = 11^2 = 121 \]