Question

rationalise
$\frac{1}{ \sqrt{5} + \sqrt{6} - \sqrt{11} }$

Answer 1

Q. Rationalize 1 / ( √5 + √6 - √11 ).

Solution :

= 1 ÷ ( √5 + √6 - √11 )

= 1 ÷ [ ( √5 + √6 ) - √11 ]

By multiplying numerator and denominator by [ ( √5 + √6 ) + √11 ].

= 1 [ ( √5 + √6 ) + √11 ] ÷ [ ( √5 + √6 ) - √11 ] [ ( √5 + √6 ) + √11 ]

= [ ( √5 + √6 ) + √11 ] ÷ [ ( √5 + √6 )² - ( √11 )² ]

= [ √5 + √6  + √11 ] ÷ [ (√5)² + (√6)² + 2 × √5 × √6 - (√11)² ]

= ( √5 + √6 + √11 ) ÷ ( 5 + 6 - 11 + 2√30 )

= ( √5 + √6 + √11 )÷ ( 2√30 )

By multiplying numerator and denominator by √30.

= √30 ( √5 + √6 + √11 ) ÷ ( 2√30 )√30

= ( √150 + √180 + √330 ) ÷ ( 2 × 30 )

=[( √(2 × 3 × 5 × 5 ) + √( 2 × 2 × 3 × 3 × 5 ) + √330 ] ÷ 60

= ( 5√6 + 6√5 + √330 ) / 60.