If `a lt 0, b gt 0`, then `sqrt(a)sqrt(b)` equal to

Options

A. `-sqrt(|a|b)`
B. `sqrt(|a|b )` i
C. `sqrt(|a|b)`
D. none of these

Answer

B

Explanation

Verify by selecting particular of a and b.
Let a = - 9 and b = 4. Then
`sqrt (a)sqrt(b) = sqrt(-9)sqrt(4) = (3i)(2) = 6i`
From option (1), we have
`-sqrt(|a|b) = - sqrt(|-9| xx 4) = - sqrt(36) = - 6 `
Form option (2), we have
`sqrt(|a|b)i = sqrt(|-9| xx ) i = 6i`