To rationalize the denominator, just multiply the numerator and denominator by its conjugate, that is, √5 - √3. It is because it abides with Difference of Two Squares in Algebra.
multiply both, the numerator and the denominator by the conjugate of the denominator i.e rt.5 - rt.3 so you get rt3 - rt5 * rt5 - rt3 over rt5 +rt3*rt5 - rt3
in the denominator, you get 5-3 = 2 which is a rational number. there you are.
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To rationalize the denominator, just multiply the numerator and denominator by its conjugate, that is, √5 - √3. It is because it abides with Difference of Two Squares in Algebra.
(√3 - √5) / (√5 + √3)
=(√3 - √5)(√5 - √3) / (√5 + √3)(√5 - √3)
=(√15 -√9 -√25+√15) / (√25 -√15 +√15 -√9)
=( -8 + 2√15 ) / 2
= -4 + √15
(â3 - â5) / (â5 + â3)
(â3 - â5)(â5 - â3) / (â5 + â3)(â5 - â3)
= (â15 - 5 - 3 + â15) / (5 - 3)
= (2â15 - 8) / (2)
= â15 - 4
multiply both, the numerator and the denominator by the conjugate of the denominator i.e rt.5 - rt.3 so you get rt3 - rt5 * rt5 - rt3 over rt5 +rt3*rt5 - rt3
in the denominator, you get 5-3 = 2 which is a rational number. there you are.
(sqrt(3)-sqrt(5))*(sqrt(3)-sqrt(5))
___________________________ =
(sqrt(3)+sqrt(5))*(sqrt(3)-sqrt(5))
3-2(sqrt(3)sqrt(5))+5
_________________ =
-2
= (sqrt(3)sqrt(5))-4