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

1 Answer
Johnson Z.
Mar 28, 2016

(5+sqrt(3))/11

Explanation:

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

2/(5-sqrt(3))

=2/(5-sqrt(3))((5+sqrt(3))/(5+sqrt(3)))

2. Simplify the numerator.

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

3. Simplify the denominator.

=(10+2sqrt(3))/(25-3)

=(10+2sqrt(3))/22

4. Factor out 2 from the numerator and denominator.

=(2(5+sqrt(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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