Question

Which represents a rational Number and how can you tell?
`√(17) √(36) √(50) √(101)`

Answer 1

`\bf \begin{array}{llll} √(17)\\\\ √(101) \end{array}\impliedby \textit{17 and 10 are both prime numbers} \\\\\\ √(36)\implies √(6^2)\implies \pm 6 \\\\\\ √(50)\implies √(25\cdot 2)\implies √(5^2\cdot 2)\implies 5√(2)\impliedby \textit{2 is a prime number}`

if a number is a prime number, it has no two equal factors that can produce a product of such a number, and therefore such value is an irrational number.

now, the last one, 5 is being multiplied by an irrational, and therefore the product will yield the same irrational, just a bit larger.

so, the only rational there is the ±6 really.