Checkpoint: Multiplying Radicals Solution

Simplify.

$\sqrt[4]{12 a^{3} b^{2} c} \cdot \sqrt[4]{27 a b^{3} c^{2}}$

$12 = 2^{2} \cdot 3, 27 = 3^{3} \sqrt[4]{2^{2} 3^{4} a^{4} b^{5} c^{3}} 2^{\frac{2}{4}} 3^{\frac{4}{4}} a^{\frac{4}{4}} b^{\frac{5}{4}} c^{\frac{3}{4}} 2^{\frac{2}{4}} {3^{1}}^{} {a^{1}}^{} b^{1 \frac{1}{4}} c^{\frac{3}{4}} 3 |a b| \sqrt[4]{2^{2} b c^{3}} 3 |a b| \sqrt[4]{4 b c^{3}}$

Note

Q: Why do some problems still have a radical expression when simplified?

A: Because there was not an exact root for that base.