Question

Somu says” \[\dfrac{{\sqrt 3 }}{1}\]is a rational number” do you agree with Somu? Give reasons.

Answer 1

Hint: A rational number is a no. which can be expressed as a ratio of two integers or in simple fraction, for example $ 4 $ which be written as $ \dfrac{4}{1} $ which is the simplest form. Whereas an Irrational no. is a number which cannot be expressed in the simplest ratio. For example, $ \pi $ – the value of $ \pi $ after decimal is continuous, which is difficult to be expressed as a simple fraction.

Complete step-by-step answer:
We are given with the no. \[\dfrac{{\sqrt 3 }}{1}\], which we can also write as \[\sqrt 3 \] because when any no. is divided by \[1\], we get the same value. So, when \[\dfrac{{\sqrt 3 }}{1}\]is divided by \[1\] it gives \[\sqrt 3 \].
Now, the value of \[\sqrt 3 \]on calculating we get:
\[\sqrt 3 = {\text{ }}1.732050807568877\] ‬(etc) and so on.
Try to convert this value into the simplest form but this value of \[\sqrt 3 \] is difficult or quite impossible to be expressed as the simplest fraction or ratio of two integers. So, these types of numbers are irrational.
So, \[\sqrt 3 \]is an irrational no.
Since,\[\sqrt 3 \]is an irrational no. So, \[\dfrac{{\sqrt 3 }}{1}\]is also an irrational no.
Therefore, Somu’s statement that “\[\dfrac{{\sqrt 3 }}{1}\] is a rational number “is wrong and I don’t agree with this statement because it’s an Irrational number not a rational number.

Note: Always remember the difference between rational and irrational numbers.
Before coming to the conclusion, always check the number by converting it into the simplest ratio form. If it’s in simplest form or ratio, then it is a rational number otherwise it’s an irrational number.