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5+√2/4+√8
can be written in the form
where r and s are both integers.
What are the values of r and s?
r-s√2/4

Sagot :

Devishri1977idn

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.

   [tex]\sf \sqrt{8}=\sqrt{2*2*2} = 2\sqrt{2}\\[/tex]

[tex]\sf \dfrac{5+\sqrt{2}}{4}+\sqrt{8}= \dfrac{5+\sqrt{2}}{4}+ 2\sqrt{2}[/tex]

          Find LCM and simplify

                     [tex]\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}\\\\[/tex]

 [tex]\sf \boxed{r=5}\\\\\boxed{s =-9}[/tex]

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