Which ones are irrational numbers?

timer Asked: Dec 6th, 2015
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School: Purdue University

Thank you for the opportunity to help you with your question!

First we should know what are rational no.s

Rational no.s are numbers which can be expressed in the form of (p/q) where p and q are integers and q is not equal to 0.

so, for a)   3/7 is a rational no. because 3/7 = p/q  and 7 is not 0 . so 4/7 is rational no.

c) ​4 =2 . therefore our no. becomes 21/2 =p/q  and 2 is not 0.  so 21/​√​4  is rational no.

e)  -13 =  ((-13)/1) =p/q   where -13 and 1 are integers and 1 is not 0 . so -13 is rational.

Now, any number in which the number after the decimal never stops or repeat is irrational number.

example   √​2 =0.414......  and it continues and nobody remembers what's coming next .

so all non perfect square numbers under root are irrational numbers.

so  b)  30 = 5*6   since 30 is not a perfect square.  therefore √30 is irrational no.

d) as for Pi ,  Pi = 3.1415......  and never repeats therefore pi is irrational no.

Please let me know if you need any clarification. I'm always happy to answer your questions.

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