How do you rationalize the denominator and simplify sqrt(3)/(sqrt(7)-2)?

1 Answer
lechugamaestro19
Mar 2, 2018

(sqrt21+2sqrt3)/3

Explanation:

To rationalize the denominator, the best move is to multiply the numerator and denominator by the reciprocal of the denominator (which is the denominator but with the middle sign reversed).

sqrt3/(sqrt7-2) * color(blue)((sqrt7+2)/(sqrt7+2))

(sqrt(3)(sqrt(7)+2))/((sqrt(7)-2)(sqrt(7)+2)

From here, we can simplify the numerator and denominator.

sqrt(alpha)sqrt(beta)=sqrt(alphabeta) -> sqrt3sqrt7=sqrt21

sqrt3(sqrt7+2)=color(red)(sqrt21+2sqrt3)

(sqrt7-2)(sqrt7+2) = 7+cancel(2sqrt7-2sqrt7)-4 = color(red)3

sqrt3/(sqrt7-2)=color(red)((sqrt21+2sqrt3)/3)

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