Solve for: square root of 288

Expression: $\sqrt{288}$

Prime factorization of $288:{\quad}2^{5}\cdot 3^{2}$

$=\sqrt{2^{5}\cdot 3^{2}}$

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

$=\sqrt{2^{4}\cdot 2\cdot 3^{2}}$

$\sqrt{2^{4}\cdot 2\cdot 3^{2}}=\sqrt{2^{4}}\sqrt{2}\sqrt{3^{2}}$

$=\sqrt{2^{4}}\sqrt{2}\sqrt{3^{2}}$

$\sqrt{2^{4}}=4$

$=4\sqrt{2}\sqrt{3^{2}}$

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

$=4\sqrt{2}\cdot 3$

Multiply the numbers: $ 4\cdot 3=12$

$=12\sqrt{2}$