What is the square root of -16 times the square root of -10?

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What is the square root of -16 times the square root of -10?

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Answer 1 · 2018-05-19T16:41:17

$- 4 \sqrt{10}$ $-4sqrt(10)$

Explanation:

By definition of imaginary numbers: $i = \sqrt{- 1}$ $i = sqrt(-1)$

$\sqrt{- 16} = 4 \cdot \sqrt{- 1} = 4 i$ $sqrt(-16) = 4*sqrt(-1) = 4i$

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

$i^{2} = i \cdot i = \sqrt{- 1} \cdot \sqrt{- 1} = {(\sqrt{- 1})}^{2} = - 1$ $i^2=i*i= sqrt(-1) * sqrt(-1) = (sqrt(-1))^2 = -1$

so:

$4 i \cdot \sqrt{10} i = 4 \sqrt{10} \cdot i^{2} = 4 \sqrt{10} \cdot (- 1) = - 4 \sqrt{10}$ $4i * sqrt(10)i = 4sqrt(10)* i^2 = 4sqrt(10)* (-1) = -4sqrt(10)$

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What is the square root of -16 times the square root of -10?

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