Question

which is greater sqrt17 -sqrt12 or sqrt11-sqrt6

Answer 1

Hi ,

It is a very good question ,

i ) sqrt17 - sqrt12

= ( sqrt17 - sqrt12 )/1×(sqrt17+sqrt12)/(sqrt17+sqrt12)

= [ (sqrt17)^2 - (sqrt12)^2 ] / (sqrt17 + sqrt12)

=( 17 - 12 )/( sqrt17 + sqrt12 )

= 5 / ( sqrt17 + sqrt12 ) -------( 1 )

ii ) sqrt11 - sqrt6

= (sqrt11 - sqrt6)/1 × ( sqrt11 + sqrt6 )/( sqrt11 + sqrt6 )

= [ ( sqrt11 )^2 - ( sqrt6)^2 ] / ( sqrt11 + sqrt6 )

= ( 11 - 6 ) / ( sqrt11 + sqrt6 )

= 5 / ( sqrt11 + sqrt6 ) --------( 2 )

We know that ,

(Sqrt17 + sqrt 12 ) > ( sqrt 11 + sqrt 6 )

Therefore,

1/ ( sqrt17 + sqrt12 ) < 1 / ( sqrt 11 + sqrt 6 )

5 / ( sqrt 17 + sqrt 12 ) < 5 / ( sqrt 11 + sqrt 6 )

[ from ( 1 ) and ( 2 ) ]

Therefore ,

We can easily conclude that ,

( sqrt 17 - sqrt 12 ) < ( sqrt 11 - sqrt 6 )

( sqrt 11 - sqrt 6 ) > ( sqrt 17 - sqrt 12 )

( Sqrt 11 - sqrt 6 ) is greater than ( sqrt 17 - sqrt 12 )

I hope this helps you.

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