Classify the following numbers as rational or irrational:
(i) \(2 - \sqrt5\)
(ii) \((3 + \sqrt23) - \sqrt23\)
(iii) \(\frac{2 \sqrt{7}} { 7 \sqrt7}\)
(iv) \(\frac{1}{\sqrt{2}}\)
(v) 2π
Classify the following numbers as rational or irrational:
(i) \(2 - \sqrt5\)
(ii) \((3 + \sqrt23) - \sqrt23\)
(iii) \(\frac{2 \sqrt{7}} { 7 \sqrt7}\)
(iv) \(\frac{1}{\sqrt{2}}\)
(v) 2π
Solution and Explanation
(i) \(2 - \sqrt5\) = 2-2.2360679…
=-0.2360679…
As the decimal expansion of this expression is non-terminating non-recurring, therefore,
it is an irrational number.
(ii) \((3 + \sqrt23) - \sqrt23\) \(=3=\frac{3}{1}\)
As it can be represent in \(\frac{p}{q}\)
(iii) \(\frac{2 \sqrt{7}} { 7 \sqrt7}=\frac{2}{7}\)
As it can be represent in \(\frac{p}{q}\)
(iv) \(\frac{1}{\sqrt{2}}=\frac{\sqrt2}{2}\)=0.7071067811…
As the decimal expansion of this expression is non-terminating non-recurring,
therefore, it is an irrational number.
(v) 2π = 2(3.1415 …) = 6.2830 …
As the decimal expansion of this expression is non-terminating non-recurring, therefore,
it is an irrational number.
Top CBSE Class IX Mathematics Questions
Top CBSE Class IX Questions
- The following table gives the lifetimes of 400 neon lamps:
Length (in hours)
Number of lamps
300 − 400
14
400 − 500
56
500 − 600
60
600 − 700
86
700 − 800
74
800 − 900
62
900 − 1000
48
(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a lifetime of more than 700 hours? - Give an example to show that even as a young girl Santosh was not ready to accept anything unreasonable.
- Where was Abdul Kalam’s house?
- What do you think Dinamani is the name of? Give a reason for your answer.
Why was Santosh sent to the local school?