Question

express in simplest radical form.
\sqrt{20}\sqrt{24}

Explanation:

Step1: Multiply the radicands

Using the property $\sqrt{a}\sqrt{b}=\sqrt{ab}$, we have $\sqrt{20}\sqrt{24}=\sqrt{20\times24}$. Calculate $20\times24 = 480$, so it becomes $\sqrt{480}$.

Step2: Factor the radicand

Factor 480 into prime factors: $480 = 16\times30$. Since 16 is a perfect square, we can rewrite $\sqrt{480}$ as $\sqrt{16\times30}$.

Step3: Simplify the square root

Using the property $\sqrt{ab}=\sqrt{a}\sqrt{b}$ (where $a = 16$ and $b = 30$), we get $\sqrt{16}\times\sqrt{30}$. Since $\sqrt{16}=4$, this simplifies to $4\sqrt{30}$.

Answer:

$4\sqrt{30}$