Question

question
express in simplest radical form.
\\(\sqrt{2}\sqrt{20}\\)

Explanation:

Step1: Use the property of radicals $\sqrt{a}\sqrt{b}=\sqrt{ab}$

$\sqrt{2}\sqrt{20}=\sqrt{2\times20}$

Step2: Calculate the product inside the radical

$2\times20 = 40$, so we have $\sqrt{40}$

Step3: Simplify $\sqrt{40}$ by factoring out the perfect square

$40 = 4\times10$, so $\sqrt{40}=\sqrt{4\times10}$

Step4: Use the property $\sqrt{ab}=\sqrt{a}\sqrt{b}$ again

$\sqrt{4\times10}=\sqrt{4}\sqrt{10}$

Step5: Simplify $\sqrt{4}$

$\sqrt{4}=2$, so we get $2\sqrt{10}$

Answer:

$2\sqrt{10}$