# How do you simplify (7sqrt(-3))(2sqrt(-27))?

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#### Explanation

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#### Explanation:

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Sarah Share
Mar 8, 2018

Always deal with imaginary numbers first. Final answer: $- 126$

#### Explanation:

If you ignore the rule of imaginary numbers which states that $\sqrt{- 1} =$$i$ and ${i}^{2}$=-1, you would be tempted to multiply all terms together to get $14 \sqrt{81} = 14 \cdot 9 = 126$ ... which would be incorrect.

To keep the validity of the complex number system, always deal with the imaginary part first. To do this, rewrite the equation:

$\left(7 \sqrt{3} \cdot \sqrt{- 1}\right) \left(2 \sqrt{27} \cdot \sqrt{- 1}\right) = \left(\sqrt{- 1} \cdot \sqrt{- 1}\right) \left(7 \sqrt{3} \cdot 2 \sqrt{27}\right)$

Now you can multiply terms within the parentheses.

$\left(\sqrt{- 1} \cdot \sqrt{- 1}\right) = i \cdot i = {i}^{2} = - 1$

and

$\left(7 \sqrt{3} \cdot 2 \sqrt{27}\right) = 14 \sqrt{81} = 14 \cdot 9 = 126$

Multiply these together and you get $126 \cdot - 1 = - 126$

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