How do you simplify #18 /(sqrt(5) - 3 sqrt (5))#?

1 Answer
Apr 21, 2016

Answer:

# = (- 9 sqrt5)/ 5#

Explanation:

#18 / ( sqrt5 - 3 sqrt5 )#

Rationalizing the expression , by multiplying it with the conjugate of the denominator : #color(blue)(sqrt5 + 3 sqrt5#

#(18 * (color(blue)(sqrt5 + 3 sqrt5) ))/ (( sqrt5 - 3 sqrt5 ) * color(blue)((sqrt5 + 3 sqrt5))#

# = (18 * (color(blue)(sqrt5)) + 18 * color(blue)((3 sqrt5)) )/ (( sqrt5 - 3 sqrt5 ) * color(blue)((sqrt5 + 3 sqrt5))#

  • Applying property #color(blue)((a-b)(a+b) = a ^2 - b^2# to the denominator.

# = (18sqrt5 + 54sqrt5)/ (sqrt(5^2 )- (3 sqrt5 )^2 )#

# = (18sqrt5 + 54sqrt5)/ (5 - (9 * 5) )#

# = (18sqrt5 + 54sqrt5)/ (5 - 45)#

# = (18sqrt5 + 54sqrt5)/ (- 40)#

# = (sqrt5(18 + 54))/ (- 40)#

# = (sqrt5(72))/ (- 40)#

# = (sqrt5(cancel72))/ (- cancel40)#

# = (sqrt5(9))/ (- 5)#

# = (- 9 sqrt5)/ 5#