Please help with pure imaginary number questions?

Question

1) sqrt of -2 times sqrt of -5

2)sqrt of -11 minus sqrt of -144

Answer 1

1) sqrt(-2) = sqrt(-1) x sqrt(2) = i x sqrt(2)

sqrt(-5) = sqrt(-1) x sqrt(5) = i x sqrt(5)

so

sqrt(-2) x sqrt(-5) = i x i x sqrt(2) x sqrt(5) = (-1) x sqrt(10) = -sqrt(10)

2) is done the same way.

HTH

Charles

Answer 2

1) sqrt(10)

2)i*(sqrt (11)-12)

Answer 3

1) √-2 x √-5 = √-10 = √-1√10 = i√10

2) √-11 - √-144 = i√11 - 12i = (√11 - 12)i