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Rationalise the denominator of the following expression, simplifying your answer as much as possible

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2 Answers

 5/ (6 - 9 √2 ) 
 
 
 5 / ( 6 - 9√2) * ( 6 +9√2) /( 6 + 9√2 )
 
    ( 30 + 45 √2 ) / ( 36 - 162) =
 
      -30/126 + 45√2/ 126 =
      
       -5/21  + 5√2/14
 

Comments

2nd term should be negative
Should write :    5 / ( 6 - 9 √2 ) , enclose the entire denominator in parenthesis, the way you feed into calculator.
I meant in your answer.
5/(6-9√2) = (5/3)(1/(2-3√2)) * (2+3√2)/(2+3√2)
 
= (5/3)((2+3√2)/((2+3√2)(2-3√2)))
 
= (5/3)((2+3√2)/(4-6√2+6√2-18))
 
= (5/3)((2+3√2)/(-14))
 
= (5/3)(-1/7-(3√2)/14)
 
= -5/21-(5√2)/14