How do you rationalize the denominator and simplify $(sqrt6)/(sqrt5 - sqrt3)$ ?

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Answer 1 · 2016-03-29T16:44:41

$= (sqrt30 + 3sqrt2)/ 2$

$(sqrt6) / (sqrt5 - sqrt3)$

Rationalizing the expression by multiplying the expression, by the conjugate of the denominator $(sqrt5 + sqrt3)$ .

$(sqrt6 * color(blue)( (sqrt5 + sqrt3))) / ((sqrt5 - sqrt3) * color(blue)( (sqrt5 + sqrt3))$

$(sqrt6 * sqrt5 + sqrt6 * sqrt3)/ ((sqrt5 - sqrt3) * color(blue)( (sqrt5 + sqrt3))$

Applying property : $color(blue)((a-b)(a+b) = a ^2 - b ^2$ , to the denominator.

$= (sqrt30 + sqrt18)/ (sqrt5 ^ 2 - sqrt3 ^2 )$

Simplifying $sqrt 18= sqrt ( 2 * 3 * 3 ) = 3 sqrt2$

$= (sqrt30 + 3sqrt2)/ (5 - 3 )$

$= (sqrt30 + 3sqrt2)/ 2$

How do you rationalize the denominator and simplify (sqrt6)/(sqrt5 - sqrt3)(sqrt6)/(sqrt5 - sqrt3)?