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Chapter 4: Problem 90

Describe the error. $$ \sqrt{-6} \sqrt{-6}=\sqrt{(-6)(-6)}=\sqrt{36}=6 $$

Short Answer

Expert verified
The error is in misunderstanding how to deal with square roots of negative numbers. The correct answer should be -6, not 6.

Step by step solution

01

Spot the Misstep

Look at the equation \(\sqrt{-6} \sqrt{-6}=\sqrt{(-6)(-6)}=\sqrt{36}=6\). The error is in the step \(\sqrt{-6} \sqrt{-6}=\sqrt{(-6)(-6)}\). It is incorrect to directly multiply the numbers underneath two square roots if they are negative.
02

Understand the Correct Method

When multiplying two square roots containing negative numbers, the square root signs must remain. They are calculated independently, first by taking the square root of the absolute value of the number and then attaching an imaginary 'i'. Hence, \(\sqrt{-6} = \sqrt{6}i\).
03

Correct Calculation

Substitute correct values back into the equation. The correct calculation should be \(\sqrt{-6} \sqrt{-6} = (\sqrt{6}i) (\sqrt{6}i) = -6\).

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Most popular questions from this chapter

In Exercises 1-24, use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. $$ (2+5 i)^{6} $$

In Exercises 1-24, use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. $$ (2+2 i)^{6} $$

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