How do you rationalize the denominator and simplify #1/(5+sqrt7)#?

1 Answer
Apr 5, 2016

Answer:

# = (5 - sqrt7) / 18#

Explanation:

#1 / ( 5 +sqrt7#

We rationalise the expression by multiplying it by the conjugate of the denominator. # color(blue)( ( 5 - sqrt7)#

# = (1 * color(blue)(( 5 - sqrt7))) / (( 5 +sqrt7) * color(blue)( ( 5 - sqrt7))#

# = (1 * color(blue)(( 5)) + 1 * color(blue)(( - sqrt7))) / (( 5 +sqrt7) * color(blue)( ( 5 - sqrt7))#

# = (5 - sqrt7) / (( 5 +sqrt7) * color(blue)( ( 5 - sqrt7))#

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

# = (5 - sqrt7) / (( 5 ^2 - (sqrt7)^2)#

# = (5 - sqrt7) / (25 - 7)#

# = (5 - sqrt7) / 18#