Question

Simplify the following. √(-128) √(-16) If possible, can I get a step-by-step?

Answer 1

that's \[(i \sqrt{128} )(i \sqrt{16})\]

i times i = i^2 = -1
\[-(\sqrt{128})(\sqrt{16})\]
\[-\sqrt{(128)(16)}\]
\[-4\sqrt{128}\]
\[-4\sqrt{(64)(2)}\]
\[-(4)(8)\sqrt{2}\]
\[-32\sqrt{?}\]

Answer 2

this used the complex number property of -1 = i^2

\[\sqrt{-128} = \sqrt{64 \times i^2 \times 2}\]

giving \[8i \sqrt{2}\]

\[\sqrt{-16} = \sqrt{16 \times i^2} = 4i\]

Answer 3

Is this correct?

√(-128) √(-16)

=√(-1*128) √(-1*16)

=√(-1)*√128 √(-1)*√16

=i√128 i√16

=i^2 √(128*16)

=-√2048

=-√(1024*2)

=-√1024*√2

=-32*√2

√(-128) √(-16)=32*√2

Answer 4

yes...only with -..you forgot that

Answer 5

ah, thank you. forgot the negative. -facepalms- lol