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Chapter 0: Problem 6

Evaluate each expression or indicate that the root is not a real number. $$\sqrt{-25}$$

Short Answer

Expert verified
The square root of -25 is \(5i\)

Step by step solution

01

Understanding Imaginary Numbers

In the context of mathematics, the square root of a negative number does not result in a real number. Instead, it results in an imaginary number. The unit of imaginary numbers is \(i\), where \(i^2 = -1\). Therefore, \(\sqrt{-1} = i \).
02

Applying the Imaginary Number Rule

We can treat the -25 as -1 multiplied by 25, so \(\sqrt{-25} = \sqrt{-1*25}\). According to the rules of square roots,\(\sqrt{-1*25} = \sqrt{-1} * \sqrt{25}\). Applying the imaginary unit rule, \(\sqrt{-1}\) is \(i\), and \(\sqrt{25}\) is 5.
03

Final Answer

So, the square root of -25 is \(5i\)

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Most popular questions from this chapter

Explain how to convert from scientific to decimal notation and give an example.

Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime of 80 years. Round the decimal factor in your scientific notation answer to two decimal places.

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{\frac{1}{2}} y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}}\right)^{-4} $$

a. Use a calculator to approximate \(\sqrt{300}\) to two decimal places. b. Use a calculator to approximate \(10 \sqrt{3}\) to two decimal places. c. Based on your answers to parts (a) and (b), what can you conclude?

Evaluate each expression without using a calculator. $$16^{-\frac{5}{2}}$$
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