Multiplying Radicals

**jesse** · May 20th 2011, 06:52 PM

$\sqrt{-12}\times\sqrt{-27}$

My book gives -18 as the answer. Is it correct?

**johnny** · May 20th 2011, 07:01 PM

√-12 × √-27 = √12i × √27i = 2√3i × 3√3i = 6√3²i² = 6 × 3 × -1 = 18 × -1 = -18, hence correct.

**jesse** · May 20th 2011, 07:04 PM

I see... I was making a simple mistake, again and again. Thanks for your help.

**Diemo** · May 20th 2011, 07:05 PM

Yes

Given $\sqrt{-1} = i$ then you have

$\sqrt{-1}\times \sqrt{-27} = \sqrt{12}i\times{\sqrt{27}i = \sqrt{12}\times\sqrt{27}\times i^2 = \sqrt{12}\times\sqrt{27}\time(-1) = -\sqrt{12}\times\sqrt{27}$

Beaten too it

**jesse** · May 20th 2011, 07:08 PM

Thanks anyway.

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