Geometric mean of 11 and 1331?

Question

anonymous · Answer

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

anonymous · Answer

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?

jamesj · Answer

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.

jamesj · Answer

*teacher's

anonymous · Answer

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

jamesj · Answer

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

anonymous · Answer

Ohh, okay. Thank you.

jamesj · Answer

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