Question

is the number \\(\sqrt{19} \cdot -1\\) rational or irrational? \
rational \
irrational \
submi

Explanation:

Step1: Analyze √19

A rational number can be expressed as \(\frac{p}{q}\) where \(p,q\) are integers and \(q
eq0\). The square root of a non - perfect square positive integer is irrational. Since 19 is not a perfect square (\(4^2 = 16\), \(5^2=25\) and \(16<19<25\)), \(\sqrt{19}\) is irrational.

Step2: Analyze the product with - 1

The product of a non - zero rational number and an irrational number is irrational. Here, we are multiplying \(\sqrt{19}\) (irrational) by \(- 1\) (rational, non - zero). So \(\sqrt{19}\times(-1)=-\sqrt{19}\) is irrational.

Answer:

irrational