Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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 :

devishri1977

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]

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.