Whats the square root of negative 8 times the square root of negative 10?

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Whats the square root of negative 8 times the square root of negative 10?

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Answer 1 · 2015-09-22T02:19:43

This is written as:

$\sqrt{- 8} \sqrt{- 10}$ $sqrt(-8)sqrt(-10)$

What you can do is factor out the two $\sqrt{- 1}$ $sqrt(-1)$ and multiply them, canceling the square root, but not changing the sign of the number under it:

$\sqrt{- 8} \sqrt{- 10} = \sqrt{- 1} \cdot \sqrt{8} \cdot \sqrt{- 1} \cdot \sqrt{10}$ $sqrt(-8)sqrt(-10) = sqrt(-1)*sqrt(8)*sqrt(-1)*sqrt(10)$

$= - \sqrt{80}$ $= -sqrt(80)$

$= - \sqrt{16 \cdot 5}$ $= -sqrt(16*5)$

$= - 4 \sqrt{5}$ $= color(blue)(-4sqrt5)$

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Whats the square root of negative 8 times the square root of negative 10?

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