Question

Classify the following number as rational or irrational \[\sqrt {27} \].

Answer 1

Hint: To know if the given number is rational or irrational, we need to simply try to make it fractional of two integers. If we are getting its fractional value containing two integers, then it is rational and if we are not getting its fractional value or decimal value with terminating term then it will be irrational.

Complete step-by-step solution:
When a number is in the form of \[\dfrac{a}{b}\] where we consider \[a\] and \[b\] as integers, and \[b\] is not equal to \[0\] then we say that the number is rational.
And when a number cannot be expressed as a fraction of two integers then we say that the number is irrational.
Now let us look at the given number that is \[\sqrt {27} \]. When we express \[\sqrt {27} \] in decimal form, we get:
\[ \Rightarrow \sqrt {27} = 5.196...\]
Here we have written 3 terms after decimal, but is actually a never ending decimal. It is also called as a non-terminating decimal with no repeating numbers.
The number \[5.196...\]. can't be written in the \[\dfrac{a}{b}\] form.
Therefore, \[\sqrt {27} \] is an irrational number.

Note: In Mathematics, a rational number may be a fraction or a decimal or a percentage which is a part of a larger whole. It is a number that cannot be expressed as a two-integer ratio (or cannot be expressed as a fraction).