Question

Classify the below expression as rational or irrational 2 root 7 - 3 root 7

Answer 1

irrational

Explanation

$2\sqrt{7}-3\sqrt{7}$

Step 1

simplify

$\begin{gathered} 2\sqrt{7}-3\sqrt{7} \\ 2\sqrt{7}-3\sqrt{7}=\left(2-3\right)\sqrt{7} \\ 2\sqrt{7}-3\sqrt{7}=(-)\sqrt{7} \\ 2\sqrt{7}-3\sqrt{7}=-\sqrt{7} \end{gathered}$

Step 2

A rational expression is the ratio of two polynomials. If f is a rational expression then f can be written in the form a/b where a and b are polynomials

$\begin{gathered} 2\sqrt{7}-3\sqrt{7}=-\sqrt{7} \\ -\sqrt{7}=-2.64575131106 \end{gathered}$

It is an irrational number because evaluating √7 gives a non recurring, non terminating decimal number

it is impossible to find a value for –√7 which can be represented as a/b where a & b are integers.

so, the answer is

irrational

I hope this helps you