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9-12 Integrated Math 3 Unit 3 Lesson 10

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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

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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 Lesson 16

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Unit 3, Lesson 10

Solving Radical Equations (Optional)

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Integrated Math 3

Practice

Problem 1

Find the solution(s) to each of these equations, or explain why there is no solution.

\(\sqrt{x+5}+7 = 10\)
\(\sqrt{x-2}+3=\text-2\)

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Problem 2

For each equation, decide how many solutions it has and explain how you know.

\((x-4)^2= 25\)
\(\sqrt{x-4} = 5\)<
\(x^3 -7 = \text-20\)
\(6 \boldcdot \sqrt[3]{x} = 0\)

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Problem 3

The volume of a regular tetrahedron (a pyramid made from 4 equilateral triangles) with side length \(s\) is given by the formula \(V = \frac{1}{6\sqrt{2}} \boldcdot s^3\).

Solve this equation for \(s\) to get the side length in terms of the volume.
If the volume of a regular tetrahedron is \(18\sqrt{2}\) cubic centimeters, what is the length of one of the sides of the tetrahedron?

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Problem 4

Here are the steps Tyler took to solve the equation \(\sqrt{x+3}=\text-5\).

\(\begin{align} \sqrt{x+3} & =\text-5 \\ x+3 &=25 \\ x &=22 \\ \end{align} \)

Check Tyler’s answer: Is the equation true if \(x=22\)? Explain or show your reasoning.
What mistake did Tyler make?

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Problem 5

ForLesson 3: Exponents That Are Unit Fractions

Complete the table. Use powers of 16 in the top row and radicals or rational numbers in the bottom row.

\(16^1\)		\(16^{\frac13}\)			\(16^{\text-1}\)
	4		1	\(\frac14\)	\(\frac{1}{16}\)

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Problem 6

ForLesson 9: Cubes and Cube Roots

Which are the solutions to the equation \(x^3=35\)?

\(\sqrt[3]{35}\)
\(\text-\sqrt[3]{35}\)
both \(\sqrt[3]{35}\) and \(\text-\sqrt[3]{35}\)
The equation has no solutions.

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Lesson 10 Resources

Student Materials