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9-12 Integrated Math 2 Unit 6 Lesson 7

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 •Integrated Math 2 Integrated Math 3

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7 Unit 8

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 •Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15

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Unit 6, Lesson 7

A New Kind of Number

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Integrated Math 2

Practice

Problem 1

Select all the true statements.

\(\sqrt{\text-1}\) is an imaginary number.
There are no real numbers that satisfy the equation \(x=\sqrt{\text-1}\).
Because \(\sqrt{\text-1}\) is imaginary, no one does math with it.
The equation \(x^2 = \text-1\) has real solutions.

\(\sqrt{\text-1} = \text-1\) because \(\text-1 \boldcdot \text-1 = \text-1\).

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Problem 2

Plot each number on the real number line, or explain why the number is not on the real number line.

\(\sqrt{4}\)
\(\text- \sqrt{4}\)
\(\sqrt{\text-4}\)
\(\sqrt{8}\)
\(\text- \sqrt{8}\)
\(\sqrt{\text-8}\)

<p>Number line, scale -10 to 10, by 2’s.</p>

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Problem 3

Explain why \((x-4)^2=\text-9\) has no real solutions.

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Problem 4

ForLesson 5: Negative Rational Exponents

Which value is closest to \(10^{\text- \frac12}\)?

-5
\(\frac15\)
\(\frac13\)
3

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Problem 5

ForLesson 8: Inequivalent Equations?

Which is a solution to the equation \(\sqrt{6-x}+5=10\)?

-19
19
21
The equation has no solutions.

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Problem 6

ForLesson 9: Cubes and Cube Roots

Select all equations for which -64 is a solution.

\(\sqrt{x} = 8\)
\(\sqrt{x} = \text-8\)
\(\sqrt[3]x = 4\)
\(\sqrt[3]x = \text-4\)
\(\text-\sqrt{x}=8\)
\(\sqrt{\text-x}=8\)

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Lesson 7 Resources

Student Materials