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

1 Answer
Mar 29, 2016

Answer:

# = (sqrt30 + 3sqrt2)/ 2 #

Explanation:

#(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 #