Question

Simplify: 1

1+√

2

+

2

√3+

√5 .

​

Answer 1

Answer:

We have,

1+

2

1

+

2

+

3

1

+

3

+

5

2

=

1+

2

1

×

1−

2

1−

2

+

2

+

3

1

×

2

−

3

2

−

3

+

3

+

5

2

×

3

−

5

3

−

5

=

1−2

1−

2

+

2−3

2

−

3

+

3−5

2(

3

−

5

)

=

−1

1−

2

+

−1

2

−

3

+

−2

2(

3

−

5

)

=−1+

2

−

2

+

3

−

3

+

5

=

5

−1

Hence, the value of expression is

5

−1.