HSN.RN Tutor Intake -- Rational Exponents and Real Number Properties

$9/2 = 4.5$

$\sqrt{9} = 3$

$9^2 = 81$

$2\sqrt{9} = 6$

$\sqrt[m]{a^n}$

$\sqrt[n]{a^m}$

$a^m \div a^n$

$n \cdot a^m$

$r + s = (pn + mq)/(qn)$. Since $pn + mq$ is an integer and
$qn$ is a nonzero integer, the sum is rational.

$r + s$ must be rational because both terms are positive.

$r + s$ equals a whole number whenever $p = m$ and $q = n$.

We can verify with examples: $1/2 + 1/3 = 5/6$, which is
rational, so the sum of any two rationals is rational.

$3 + \sqrt{25}$

$\sqrt{4} + \sqrt{9}$

$\frac{1}{2} + \sqrt{7}$

$0.6\overline{6} + \frac{1}{3}$