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0 votes
8.0k views
in Real Numbers by (47.9k points)
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Find any two irrational numbers between 

(i) 0.3010011000111… and 0.3020020002…

(ii) \(\frac{6}{7}\) and \(\frac{12}{13}\)

(iii) \(\sqrt{2}\) and \(\sqrt{3}\)

2 Answers

+1 vote
by (47.6k points)
selected by
 
Best answer

(i) 0.3010011000111… and 0.3020020002…

Two irrational numbers 0.301202200222 ..., 0.301303300333 ...

(ii) \(\frac{6}{7}\) and \(\frac{12}{13}\)

\(\frac{6}{7}\) = 0.857142 ...

\(\frac{12}{13}\) = 0.923076

Two irrational numbers between 

0.8616611666111…, 0.8717711777111…

(iii) \(\sqrt{2}\) and \(\sqrt{3}\)

\(\sqrt{2}\) = 1.414 ... 

\(\sqrt{3}\) = 1.732...

∴ Two irrational numbers between 1.5155…, 1.6166…

0 votes
by (128 points)

the rational numbers are:-
1) 0.3016389263...
2) 0.301999999...

 two rational numbers between √2 and √3 are 1.5 and 1.6

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