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Rationalize the denominator 2√7+√3/3√7-√3​
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1 vote
Rationalize the denominator 2√7+√3/3√7-√3​

User Yuriy Seredyuk
by
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2 Answers

4 votes

Answer:


(2 √(7) + √(3))/(3 √(7) - √(3) ) = (2 √(7) + √(3))/(3 √(7) - √(3) ) . (3 √(7) + √(3) )/(3 √(7) + √(3) ) \\ \\ = ((2 √(7) + 3)(3 √(7) + √(3)) )/((3 √(7) - 3)(3 √(7) + √(3) ) ) \\ \\ = ((42 + 2 √(21) + 9 √(21) + 3 √(21) ))/(63 - 3) \\ \\ = (42 + 2√(21) + 9 √(21) + 3 √(21) )/(60)

User Dtbarne
by
8.2k points
7 votes

Answer:

  • (2√7+√3)/(3√7-√3)​ =
  • (2√7+√3)(3√7+√3)​/(3√7-√3)​(3√7+√3)​ =
  • (2*3*√7² + 2√21 + 3√21 + √3²)/(9√7² - √3²) =
  • (42 + 3 + 5√21)/(63 - 3) =
  • (45 + 5√21)/60 =
  • (9 + √21)/12
User Lord Peter
by
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