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  • The number of rational terms of   <img alt="(1+\sqrt{2}+3 \sqrt{5})^6" src="https://entrancecorner.oncodecogs.com

The number of rational terms of   (1+\sqrt{2}+3 \sqrt{5})^6  is

Option: 1

7


Option: 2

11


Option: 3

12


Option: 4

20


Answers (1)

best_answer

General term  =\frac{6 !}{r ! s ! t !}(1)^r(\sqrt{2})^s(\sqrt[3]{5})^t

If  \mathrm{s}=0, \mathrm{t}=0,3,6

\mathrm{s}=2, \mathrm{t}=0,3, \\

\mathrm{~s}=4, \mathrm{t}=0 \\

\mathrm{~s}=6, \mathrm{t}=0

hence 7 rational terms exists.

Posted by

Divya Prakash Singh

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