Question

5+√2/4+√8

Answer 1

Answer:

r = 5   ; s = -9

Step-by-step explanation:

  Radical simplification.

First simplify √8  by

• Prime factorize 8
• Make pairs of similar factor
• Take one factor out of every pair.

   $\sf \sqrt{8}=\sqrt{2*2*2} = 2\sqrt{2}$

$\sf \dfrac{5+\sqrt{2}}{4}+\sqrt{8}= \dfrac{5+\sqrt{2}}{4}+ 2\sqrt{2}$

          Find LCM and simplify

                     $\sf = \dfrac{5+\sqrt{2}}{4}+\dfrac{2\sqrt{2}*4}{1*4}\\\\ =\dfrac{5+\sqrt{2}+8\sqrt{2}}{4} \ {\bf Combine \ like\ terms} \\\\ = \dfrac{5+9\sqrt{2}}{4}$

 $\sf \boxed{r=5}\\\\\boxed{s =-9}$