Algebra 2 | Unit 3 | Lesson 9: Solving Radical Equations | Practice Problems

Find the solution(s) to each of these equations, or explain why there is no solution. \(\sqrt{x+5}+7 = 10\)

• \(x=4\)

• No solution

Find the solution(s) to each of these equations, or explain why there is no solution. \(\sqrt{x-2}+3=\text-2\)

• \(x=4\)

• No solution

For each equation, decide how many solutions it has and explain how you know. \((x-4)^2= 25\)

• 2 solutions

• 1 solution

• No solution

For each equation, decide how many solutions it has and explain how you know. \(\sqrt{x-4} = 5\)

• 2 solutions

• 1 solution

• No solution

For each equation, decide how many solutions it has and explain how you know. \(x^3 -7 = \text-20\)

• 2 solutions

• 1 solution

• No solution

For each equation, decide how many solutions it has and explain how you know. \(6 \boldcdot \sqrt[3]{x} = 0\)

• 2 solutions

• 1 solution

• No solution

Jada was solving the equation \(\sqrt{6-x}=\text-16\). She was about to square each side, but then she realized she could give an answer without doing any algebra. What did she realize?

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Here are the steps Tyler took to solve the equation \(\sqrt{x+3}=\text-5\). 1. \(\sqrt{x+3} =\text-5 \) 2. \(x+3=25 \) 3. \(x=22 \) 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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Complete the table. Use powers of 16 in the top row and radicals or rational numbers in the bottom row.

Power		Radical
\(16^1\)		\(\frac{1}{16}\)
\(16^{\frac13}\)	\(16^{\text-1}\)
	\(\sqrt[3]{16}\)	1
4	\(\frac14\)	16

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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.