Question

Which represents a rational Number and how can you tell?20%5Csqrt%7B50%7D%20%5Csqrt%7B101%7D%20" id="TexFormula1" title=" \sqrt{17} \sqrt{36} \sqrt{50} \sqrt{101} " alt=" \sqrt{17} \sqrt{36} \sqrt{50} \sqrt{101} " align="absmiddle" class="latex-formula">

Answer 1

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

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.