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=1/(3-2.828)-1/(2.828-2.645)+1/(2.645-2.449)-1/(2.449-2.236)+1/(2.236-2)

=1/(0.172)-1/(0.183)+1/(0.916)-1/(0.213)+1/(0.236)

=5.813-5-4644+5.1020-4.6948+4.237

=4.99

=5 Approximately

=1/(0.172)-1/(0.183)+1/(0.916)-1/(0.213)+1/(0.236)

=5.813-5-4644+5.1020-4.6948+4.237

=4.99

=5 Approximately

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

1/(3-√8) - 1/(√8-√7) + 1/(√7-√6) - 1/(√6-√5) + 1/(√5-2) = 51/(3-rt8)=[1/(3-rt8)]{(3+rt8)/(3+rt8)] ..... (by rationalising)

=(3+rt8)/(9-8) from ...a^2-b@=(a+b)(a-b)

=3+rt8

as first term all terms will be rationalised...so the expression becomes

3+rt8-rt8-rt7+rt7+rt6-rt6-rt5+rt5+2

then all root terms will get cancelled

=3+2=5

=(3+rt8)/(9-8) from ...a^2-b@=(a+b)(a-b)

=3+rt8

as first term all terms will be rationalised...so the expression becomes

3+rt8-rt8-rt7+rt7+rt6-rt6-rt5+rt5+2

then all root terms will get cancelled

=3+2=5