rationalizing denominators help ! 4 medals !

Question

joftheworld · Answer

attachment

tylerd · Answer

$$\sqrt{8x}$$

what could you multiply this by to get 8x?

jdoe0001 · Answer

$\bf -\cfrac{10}{\sqrt{8x}}\cdot \cfrac{\sqrt{8x}}{\sqrt{8x}}\implies -\cfrac{10{\sqrt{8x}}}{({\sqrt{8x}})^2}\implies ?$

joftheworld · Answer

that seems alot more complicated..

jdoe0001 · Answer

well... the idea being, "simplify" meaning, get rid of the pesky radical in the denominator

and the way you'd do it is by multiplying top and bottom by the denominator.... so the denominator ends up squared and thus comes out of the radical

joftheworld · Answer

which still confuses me..

jdoe0001 · Answer

well      $\bf -\cfrac{10}{\sqrt{8x}}\cdot \cfrac{\sqrt{8x}}{\sqrt{8x}}\implies -\cfrac{10{\sqrt{8x}}}{({\sqrt{8x}})^2}\implies -\cfrac{\cancel{ 10 }{\sqrt{8x}}}{\cancel{ 8 }x}\implies ?$