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

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

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Answer 1 · 2018-03-24T01:49:40

$14 \sqrt{2}$ $14sqrt(2)$

Explanation:

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

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

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

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

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

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