How do you simplify the square root of 28 times the square root of 14?

Mar 24, 2018

$14 \sqrt{2}$

Explanation:

You can rewrite each radicand as a product of its prime factors:
$\sqrt{28} \cdot \sqrt{14} = \sqrt{2 \cdot 2 \cdot 7} \cdot \sqrt{2 \cdot 7}$

You can then separate each factor into individual radicands:
$\sqrt{2 \cdot 2 \cdot 7} \cdot \sqrt{2 \cdot 7} = \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{7} \cdot \sqrt{7}$

Next multiply the square roots that have a matching pair:
$\sqrt{2} \cdot \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{7} \cdot \sqrt{7} = 2 \cdot \sqrt{2} \cdot 7$

Finally, simplify:
$2 \cdot \sqrt{2} \cdot 7 = 14 \sqrt{2}$