Question

Which of these numbers is irrational?

Answer 1

A. \[\sqrt{3}\]
B. 0.25
C. \[\frac{ 1 }{ 5 }\]
D. \[\sqrt{9}\]

Answer 2

A

Answer 3

An irrational number is one that is not periodic (meaning there is no repeating decimal number, meaning you cannot express the number as a fraction of two integers). For example, in 0.25, you can express it as 1/4, and you notice that 0.25=0.25000000... but we simply cut off the zeros.

1/5 is a fraction, so that's ok.

\(\sqrt9\) is rational (NOT irrational) because it simply gives 3, which is just an integer (you can also think of it as \(\frac{3}{1}\) or 3.0000000....

Now, can you think of a a way to express \(\sqrt3\) as a fraction of two integers? No, you cannot !!

Irrational numbers will have non-repeating decimals (there is no pattern in the repeating decimal), and such numbers are :
1) square roots (of numbers that are NOT perfect squares... meaning you cannot express them as \(a*a=a^2\)
2) \(\pi\)
3) \(e\) as in the natural number "e" = 2.71....