Question

Rationalise the denominator​

Answer 1

Answer:

Step-by-step explanation:

1 /

1+√3−√5

The rationalization of this denominator is a two-set process.

First rationalize the

√5

and then, after some simplification

rationalize the

√3

Let a =(1+√3)

So our initial stage is to rationalize the denominator of

1/ a−√5

As usual to do this we multiply the numerator and the denominator by the conjugate of the denominator:

1 /a−√5⋅a+√5

         a+√5

=  a+√5

   a2−5

Substituting

(1+√3)

back in to this expression in place of a.we get

=            1 +√3+√5

             (1+√3)2−5

=      1+√3+√5

      1+2√3+3−5

=   1+√3+√5

      2√3−1

Rationalizing this denominator (using the conjugate of 2√3−1

results in

(1+√3+√5)

(2√3−1)⋅              (2√3+1)

                             (2√3+1)

=7+3√3+√5+2√15

           11