## k.rene.s 3 years ago Simplify the number using the imaginary unit i: (square root) -28 options: a. 2(square root) -7 b. -2(square root) -7 c. i(square root) 28 d. 2i(square root) 28

1. SheldonEinstein

Ok so it is $\large{\sqrt{-28}}$ Correct?

2. CliffSedge

Factor 28 first to find the perfect square. and remember that i=√(-1)

3. k.rene.s

Yes. @SheldonEinstein

4. SheldonEinstein

$\large{\sqrt{-28} = \sqrt{-1}\sqrt{28} = \sqrt{-1} \sqrt{4*7}}$

5. SheldonEinstein

So it will be $\large{(\sqrt{-1}) 2\sqrt{7} }$

6. SheldonEinstein

Now as we know that $\large{\sqrt{-1} = i (\textbf{IOTA})}$

7. SheldonEinstein

So we have answer : $$\large{ i \sqrt{28} }$$

8. SheldonEinstein

Got it?

9. k.rene.s

Yes thanks for both of your help and Sheldon for explaining so well :)

10. SheldonEinstein

You're welcome and thanks for the appreciation.

11. CliffSedge

i√28 is not fully simplified.

12. SheldonEinstein

Options have isqrt{28}

13. SheldonEinstein

Hence no need to simplify further.

14. CliffSedge

Ah, yes. After a second look 2i√7 isn't an option.

15. SheldonEinstein

Yeah, at first I thought the same and hence simplified it further but when saw the options again , I got to see the option i sqrt{28}...