How do you rationalize the denominator and simplify #4/(6-sqrt5)#?

1 Answer
Mar 27, 2016

Answer:

#= (24 + 4 sqrt5)/ (31)#

Explanation:

# 4 / ( 6 -sqrt5)#

To rationalize the denominator, we multiply the expression , by the conjugate of the denominator.

Conjugate , of # 6 -sqrt5 = color(blue)( 6 + sqrt5#

# 4 / ( 6 -sqrt5) = (4 * (color(blue)( 6 + sqrt5))) / (( 6 -sqrt5) * color(blue)( 6 + sqrt5)#

  • Applying below mentioned property to simplify denominator:
    #color(blue)((a-b)(a+b) = a^2 - b^2#

# = (4 * (color(blue)( 6)) + 4 * (sqrt5))/ (( 6 ) ^2 -(sqrt5)^2)#

#= (24 + 4 sqrt5)/ ((36 - 5)#

#= (24 + 4 sqrt5)/ (31)#