How do you rationalize the denominator and simplify 2/(5-sqrt3)25−√3?

1 Answer
Johnson Z.
Mar 28, 2016

(5+sqrt(3))/115+√311

Explanation:

11. Multiply the numerator and denominator by the conjugate of 5-sqrt(3)5−√3, which is 5+sqrt(3)5+√3.

2/(5-sqrt(3))25−√3

=2/(5-sqrt(3))((5+sqrt(3))/(5+sqrt(3)))=25−√3(5+√35+√3)

22. Simplify the numerator.

=(10+2sqrt(3))/((5-sqrt(3))(5+sqrt(3))=10+2√3(5−√3)(5+√3)

33. Simplify the denominator.

=(10+2sqrt(3))/(25-3)=10+2√325−3

=(10+2sqrt(3))/22=10+2√322

44. Factor out 22 from the numerator and denominator.

=(2(5+sqrt(3)))/(2(11))=2(5+√3)2(11)

=(color(red)cancelcolor(black)2(5+sqrt(3)))/(color(red)cancelcolor(black)2(11))

=color(green)(|bar(ul(color(white)(a/a)(5+sqrt(3))/11color(white)(a/a)|)))

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