Question

simplify the radical with imaginary numbers:

Answer 1

\[\sqrt{-2} *\sqrt{-10}\]

Answer 2

@Hero

Answer 3

Hint: Rewrite the expression usnig \(i = \sqrt{-1}\)

Answer 4

For example \(\sqrt{-7} = \sqrt{-1 \cdot 7} = \sqrt{-1}\sqrt{7} = i\sqrt{7}\)

Answer 5

so then \[\sqrt{-2}= \sqrt{-1*2}=\sqrt{-1}*\sqrt{2}= i \sqrt{2}\]
and the same thing for -10, right?

Answer 6

Very good. Correct. Do the same for the other expression then simplify completely. It would be best to show all your work here.

Answer 7

ok so for the -10 you do
\[\sqrt{-10}= \sqrt{-1*10}= \sqrt{-1} *\sqrt{10}= i \sqrt{10}\]
so then you have \[i \sqrt{2}*i \sqrt{10}\]
and then that is \[i^2\sqrt{20 }\]

is this right so far?
because then i simplify the sqrt of 20 and i^2=-1

Answer 8

Correct. Keep going.

Answer 9

ok so then

\[i^2\sqrt{20}\]

the i^2 becomes -1 so we have
\[-1\sqrt{20}\]

and then \[\sqrt{20}= \sqrt{4}*\sqrt{5}= 2\sqrt{5}\]

and then the 2 and the -1 are outside the radical so you combine them and then you get

\[-2\sqrt{5}\]
??

Answer 10

Correct.

Answer 11

ty!