What is the square root of 12 multiplied by the square root of 6?

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What is the square root of 12 multiplied by the square root of 6?

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Answer 1 · 2015-09-17T03:53:09

$sqrt(12)sqrt(6) = 6sqrt2$

Explanation:

To evaluate $sqrt12sqrt6$ we must first remember that we can join these two roots together

$sqrtasqrtb = sqrt(ab)$ as long as they're not both negative, so
$sqrt12sqrt6 = sqrt(12*6)$

While we can just multiply these two, we know that $12 = 2*6$ , so we know that $12*6 = 2*6*6 = 2*6^2$

Therefore $sqrt(12*6) = sqrt(2*6^2)$ .
Now, since there's no additions or differences being done we can take it out of the root, but to get out it loses its square. So

$sqrt(12)sqrt(6) = 6sqrt2$

And now there's no more manipulation to be done.

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What is the square root of 12 multiplied by the square root of 6?

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