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

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Answer 1 · 2015-06-03T08:50:49

$2/(5-sqrt3)$

We can ratioinalise the denominator by multiplying the numerator and denominator of the expression by the conjugate of $5-sqrt3$

The conjugate of $5-sqrt3 = color(red)(5+sqrt3$

$=(2xxcolor(red)((5+sqrt3)))/((5-sqrt3)xxcolor(red)((5+sqrt3))$

We know that $color(blue)((a-b)(a+b)=a^2 - b^2$
so , $(5-sqrt3)xx(5+sqrt3) = 5^2- sqrt3^2 = color(blue)(25 - 3 = 22$

the expression becomes:
$(cancel2xxcolor(red)((5+sqrt3)))/cancel22$

$= (5+ sqrt3)/ 11$

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