Classify the following numbers as rational or irrational with justification: 6.412341234....... 1.919919991...... (√2+3)-(√2-5) √20/5 0.326 √72/√81 √3.61 -√2.25 2√125
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1.919919991 is irrational. It does not terminate neither does it repeat.
(2^1/2+3)-(2^1/2-5) is rational. On opening the bracket,root 2 gets cancelled
and 3+5=8 which is a rational number.
6.41234123 is rational as the digits repeat.
Root 20/5 is also irrational as it is not a perfect square.
0.326 is rational as it can be expressed as 326/10000.
Root 72 is irrational as it is not a perfect square.
Root 81 is rational as its value is 9 and it is a perfect square.
Root 3.61 is also an irrational number.
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Answer:
1.919919991 is irrational. It does not terminate neither does it repeat. (2^1/2+3)-(2^1/2-5) is rational. On opening the bracket,root 2 gets cancelled and 3+5=8 which is a rational number. 6.41234123 is rational as the digits repeat. Root 20/5 is also irrational as it is not a perfect square. 0.326 is rational as it can be expressed as 326/10000. Root 72 is irrational as it is not a perfect square. Root 81 is rational as its value is 9 and it is a perfect square. Root 3.61 is also an irrational number.
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