The simplest value of 1/{\sqrt2+\sqrt3}+1/{\sqrt3+\sqrt4}+1/{\sqrt4+\sqrt5}+1/{\sqrt5+\sqrt6} is

RRB Junior Engineer Stage 1 Model Papers 3

Question : 26 of 100

Marks: +1, -0

The simplest value of

1/{√2+√3}+1/{√3+√4}+1/{√4+√5}+1/{√5+√6}

Solution:

1/{√2+√3}=1/{√3+√2}×{√3-√2}/{√3-√2}={√3-√2}/{3-2}

=√3-√2 1/{√4+√3}

=√4-√3;1/{√4+√5}

=√5-√4;1/{√+√6}=√6-√5

∴ Expression

=√3-√2+√4-√3+√5-√4+√6-√5

=√6-√2=√2(√3-1)

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