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Chapter 2: Problem 42

Perform the indicated operations and write the result in standard form. $$\sqrt{-12}(\sqrt{-4}-\sqrt{2})$$

Short Answer

Expert verified
-4-2\sqrt{6}i

Step by step solution

01

Handle square roots of negative numbers

First, simplify \( \sqrt{-12} \) and \( \sqrt{-4} \). Using the property \( \sqrt{-a} = i\sqrt{a} \), this becomes \( 2i\sqrt{3} \) and \( 2i \), respectively.
02

Distribution

Then, distribute the multiplication of \( 2i\sqrt{3} \) into \( 2i-\sqrt{2} \). This becomes \( 4i^2 - 2\sqrt{2}i\sqrt{3} \).
03

Simplify the expression

Finally, substitute \( i^2 \) with -1 and simplify: \( 4i^2 \) becomes -4 and \( 2\sqrt{2}i\sqrt{3} \) simplifies to \( -2\sqrt{6}i \), giving a final answer of minus four minus two root six i.

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Most popular questions from this chapter

The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{x-5}{10 x-2} \div \frac{x^{2}-10 x+25}{25 x^{2}-1}$$

Solve each inequality using a graphing utility. $$2 x^{2}+5 x-3 \leq 0$$

Find the horizontal asymptote, if there is one, of the graph of rational function. $$f(x)=\frac{-3 x+7}{5 x-2}$$

Find the horizontal asymptote, if there is one, of the graph of rational function. $$h(x)=\frac{15 x^{3}}{3 x^{2}+1}$$

Solve each inequality using a graphing utility. $$\frac{1}{x+1} \leq \frac{2}{x+4}$$
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