How do you rationalize the denominator and simplify #1/(7-sqrt6)#?

1 Answer
Don't Memorise
Apr 2, 2016

#= ( 7 +sqrt6) /43#

Explanation:

#1 / (7 - sqrt6)#

We rationalise by multiplying the expression by the conjugate of the denominator, which is #color(blue)(7 +sqrt6#

#= (1 * color(blue)(( 7 +sqrt6))) /( (7 - sqrt6) * color(blue)( 7 +sqrt6)#

#= ( 7 +sqrt6) /( (7 - sqrt6) *( color(blue)( 7 +sqrt6))#

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

#= ( 7 +sqrt6) /( (7^2 - (sqrt6)^2)#

#= ( 7 +sqrt6) /( (49 - 6)#

#= ( 7 +sqrt6) /43#

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