Question

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

Answer 1

irrational

Step-by-step explanation

`2√(7)-3√(7)`

Step 1

simplify

`\begin{gathered} 2√(7)-3√(7) \\ 2√(7)-3√(7)=\left(2-3\right)√(7) \\ 2√(7)-3√(7)=(-)√(7) \\ 2√(7)-3√(7)=-√(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√(7)-3√(7)=-√(7) \\ -√(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