Find the negative square root of 48

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Find the negative square root of 48

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Hmm the one I got is -6.9

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Ok do you know how you would get that without using a calclutor?
I do not
ok thanks
  • phi
you could factor 48 into its prime factors 2*2*2*2 * 3 and look for "pairs" there are two pairs of "2's". "pull each pair out of the radical, and put only one of each out front: \[ \sqrt{2\cdot 2 \cdot 2 \cdot 2 \cdot 3}= 2\cdot 2 \sqrt{3} \] simplify 2*2 to 4 and we want the negative square root, so make it negative \[ -4 \sqrt{3} \] notice what we get if we multiply it by itself \[ -4 \sqrt{3} \cdot -4 \sqrt{3} = -4\cdot -4 \cdot \sqrt{3} \cdot \sqrt{3} \\ =16 \cdot 3 = 48 \]
ok thanks i think i understand now

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