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Chapter 2: Problem 29

Perform the indicated operations and write the result in standard form. $$\sqrt{-64}-\sqrt{-25}$$

Short Answer

Expert verified
The result of \(\sqrt{-64}-\sqrt{-25}\) is \(3i\).

Step by step solution

01

Calculate the square root of -64

To calculate the square root of -64, you separate it as \(\sqrt{-1}\) times \(\sqrt{64}\). The result is 8i, since \(\sqrt{-1}\) equals 'i' and \(\sqrt{64}\) equals 8.
02

Calculate the square root of -25

Similarly, to calculate the square root of -25, separate it as \(\sqrt{-1}\) times \(\sqrt{25}\). This results in 5i, as \(\sqrt{-1}\) equals 'i' and \(\sqrt{25}\) equals 5.
03

Perform the subtraction

Now subtract the result of \(\sqrt{-25}\) from the result of \(\sqrt{-64}\), which is \(8i - 5i\). This simplifies to 3i.

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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. $$\frac{x-\frac{1}{x}}{x+\frac{1}{x}}$$

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