Question

sqrt -6 times sqrt -18 ?

Answer 1

Do you mean, \[(\sqrt{-6})(\sqrt{-18})\]

Answer 2

Are you familiar with complex numbers?

\[(√-6)(√-18) = (6i)(18i)\]
\[= 108i^2 - 108(-1) = -108 \]

Answer 3

\[(i \sqrt{6})(i \sqrt{18})\]
\[ -\sqrt{6}\sqrt{18}\]
\[-\sqrt{108}\]
\[-6\sqrt{3}\]

Answer 4

\[ \sqrt{-6} \times \sqrt{-18}\]

Answer 5

Yes \[\LARGE{\sqrt{-6}\times\sqrt{-18}}\]\[\LARGE{=\sqrt{-6\times-18}}\]\[\LARGE{=\sqrt{108}}\]

Answer 6

@jricafort here are two \(i\) therefore it will become +

Answer 7

jricafort is correct

Answer 8

why ?

Answer 9

you are using a rule incorrectly

Answer 10

@TheViper \[i ^{2} = -1, i ^{3} = -i, i ^{4} = 1, \]

Answer 11

if \(a,b\ge 0\) then \[\sqrt{a}\sqrt{b}=\sqrt{ab}\]


this is not true is a,b<0

Answer 12

this is not true if a,b<0

Answer 13

\[\LARGE{\sqrt{-6}\times\sqrt{-18}}\]\[\LARGE{=\sqrt{-1}\times\sqrt{-1}\times\sqrt{6}\times\sqrt{18}}\]\[\LARGE{=(\sqrt{-1})^2}\times{108}\]\[\LARGE{=-1\times108=-108}\]

Answer 14

Sorry!

Answer 15

thank you everyone(:

Answer 16

No problem!

Answer 17

right @mayankdevnani :)

Answer 18

right @TheViper