How do you simplify 10 square root 6 times square root 2?

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How do you simplify 10 square root 6 times square root 2?

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Answer 1 · 2015-09-08T15:52:09

By using
$\sqrt{a} \times \sqrt{b} = \sqrt{a b}$ $sqrt(a) xx sqrt(b) = sqrt(ab)$ ,

$10 \sqrt{6} \times \sqrt{2} = 20 \sqrt{3}$ $10sqrt(6) xx sqrt(2) = 20sqrt(3)$

Explanation:

To simplify $10 \sqrt{6} \times \sqrt{2}$ $10sqrt(6) xx sqrt(2)$ we just need to keep in mind the following rule regarding radicals:

$\sqrt{a} \times \sqrt{b} = \sqrt{a b}$ $sqrt(a) xx sqrt(b) = sqrt(ab)$

This means that:

$10 \sqrt{6} \times \sqrt{2}$ $10sqrt(6) xx sqrt(2)$
$= 10 \sqrt{6 \cdot 2}$ $= 10sqrt(6*2$
$10 \sqrt{12}$ $10sqrt(12)$

From this step, we need to check if we can factor out any perfect squares from $12$ $12$ . If there is a perfect square, we can factor it out to simplify it more.

$4$ $4$ is a perfect square, and we can factor out $4$ $4$ from $12$ $12$ since $12 = 4 \times 3$ $12 = 4 xx 3$ . We just apply the rule in reverse, splitting the radical.

$10 \sqrt{12}$ $10sqrt(12)$
$= 10 \sqrt{4 \times 3}$ $=10sqrt(4 xx 3)$
$= 10 \sqrt{4} \times \sqrt{3}$ $=10sqrt(4)xxsqrt(3)$
$= 10 \times 2 \times \sqrt{3}$ $=10xx2xxsqrt(3)$
$= 20 \sqrt{3}$ $=20sqrt(3)$

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How do you simplify 10 square root 6 times square root 2?

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