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Chapter 2: Problem 56

Perform the indicated operation(s) and write the result in standard form. $$5 \sqrt{-8}+3 \sqrt{-18}$$

Short Answer

Expert verified
The result is \(19i\sqrt{2}\).

Step by step solution

01

Simplify Square Roots

Rewrite \sqrt{-8} and \sqrt{-18} in terms of 'i'. Since \sqrt{-1} = i, You can rewrite \sqrt{-8} as \( i\sqrt{8} \) and \sqrt{-18} as \(i\sqrt{18}\).
02

Simplify Further and Factor Out

The square roots can be simplified further: \(\sqrt{8} = 2\sqrt{2}\) and \(\sqrt{18} = 3\sqrt{2}\). Now you can rewrite \(i\sqrt{8}\) as \(2i\sqrt{2}\) and \(i\sqrt{18}\) as \(3i\sqrt{2}\). Then multiply them by the constants outside the square roots, hence, \(5*2i\sqrt{2} + 3*3i\sqrt{2} = 10i\sqrt{2} + 9i\sqrt{2}\).
03

Combine Like Terms

Combine the two terms to simplify the expression. \(10i\sqrt{2} + 9i\sqrt{2}= 19i\sqrt{2}\). This is the answer in standard form.

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Most popular questions from this chapter

What is a rational function?

Basic Car Rental charges \(\$ 20\) a day plus \(\$ 0.10\) per mile, whereas Acme Car Rental charges \(\$ 30\) a day plus \(\$ 0.05\) per mile. How many miles must be driven to make the daily cost of a Basic Rental a better deal than an Acme Rental?

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{2}+1}{x}$$

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

Will help you prepare for the material covered in the next section. Solve: \(2 x^{2}+x=15\)
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