Question

express in simplest radical form. \\(\sqrt{2}\sqrt{6}\\) answer attempt 1 out of 2 submit answer

Explanation:

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

$\sqrt{2}\sqrt{6}=\sqrt{2\times6}$

Step2: Simplify the product inside the radical

$2\times6 = 12$, so we have $\sqrt{12}$

Step3: Factor 12 into perfect square and other factor

$12 = 4\times3$, so $\sqrt{12}=\sqrt{4\times3}$

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

$\sqrt{4\times3}=\sqrt{4}\sqrt{3}$

Step5: Simplify $\sqrt{4}$

$\sqrt{4} = 2$, so we get $2\sqrt{3}$

Answer:

$2\sqrt{3}$