1 Answer
Solution :-
We know
(i) \( \sqrt{23}\)
\( \sqrt{23}\) = 4.795831…..
It is an irrational number
(ii) \( \sqrt{225}\) = 15
Therefore, \( \sqrt{225}\) is a rational number.
(iii) 0.3796
It is terminating decimal. Therefore, it is rational number
(iv) 7.478478….
The given number 7.478478…. is a non-terminating recurring decimal, which can be converted into \( \frac{p}{q}\) form.
While, converting 7.478478…. into \( \frac{p}{q}\) form, we get
x = 7.478478.... … (a)
1000x = 7478.478478.... … (b)
While, subtracting (a) from (b), we get
\( \cfrac{\begin{matrix}1000\mathrm x = 7478.478478...\\-\mathrm x = 7.478478....\end{matrix}}{999\mathrm x = 7471}\)
x = \( \frac{7471}{999}\)
Therefore, 7.478478…. is a rational number.
(v) 1.101001000100001....
We can observe that the number 1.101001000100001.... is a non-terminating nonrecurring decimal. Thus, non-terminating and non-recurring decimals cannot be converted into \( \frac{p}{q}\) form.
Therefore, we conclude that 1.101001000100001.... is an irrational number.
Answered by Shivani Kumari | 2 years agoRelated Questions
Visualise the representation of \( 5.3\overline{7}\) on the number line upto 5 decimal places, that is upto 5.37777.
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Find whether the following statements are true or false:
(i) Every real number is either rational or irrational.
(ii) π is an irrational number.
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