sqrt{-25}*sqrt{-4}

Question

sqrt{-25}*sqrt{-4}

anonymous · Answer

True or false is = sqrt{100}=10

callisto · Answer

$$\sqrt{-25} \times \sqrt{-4} =\sqrt{-25\times -4}  = \sqrt{100} = 10$$Is it true then?

anonymous · Answer

When I put it in wolfram it is coming up as -10 idk why...

unklerhaukus · Answer

$$\sqrt{-25}\times\sqrt{-4}$$$$=\sqrt{-1}\times\sqrt{25}\times\sqrt{-1}\times\sqrt4$$$$=5i\times2i$$$$=10i^2$$$$=-10$$

callisto · Answer

Oh... my bad :| Sorry!!!!!

anonymous · Answer

Okay, thank you...

unklerhaukus · Answer

the use of the imaginary unit   $i\equiv \sqrt{-1}$

anonymous · Answer

Thanks quick @ UncleRhaukus and Callisto for your response!!! It was greatly appreciated!!!

callisto · Answer

Sorry to ask, but when can I multiply the square root like I did and when I cannot?

unklerhaukus · Answer

i dunno i have made that mistake before too ,
i think the error is that you cant take the -1 out of the square root for some reason

callisto · Answer

In this case, I'll just rewrite the expression using imaginary unit and do the calculations then.. Thank you !!!

anonymous · Answer

You can't take the square root less than zero when it is a even root... because you get complex solutions.

anonymous · Answer

Because you can take the cube root of -1 and the cube root of -8

callisto · Answer

Hmm... I was saying multiplication...