Evaluate: square root of 27

Expression: $\sqrt{27}$

Prime factorization of $27:{\quad}3^{3}$

$=\sqrt{3^{3}}$

Apply exponent rule $a^{b+c}=a^b\cdot a^c$

$=\sqrt{3^{2}\cdot 3}$

Apply radical rule $\sqrt{ab}=\sqrt{a}\sqrt{b},\quad a\ge0, b\ge0$

$=\sqrt{3^{2}}\sqrt{3}$

Apply radical rule $\sqrt{a^2}=a,\quad a\ge0$

$=3\sqrt{3}$

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