Solving Radical Equations: IM Alg2.3.9
[url=https://im.kendallhunt.com/HS/teachers/3/3/9/preparation.html]“Solving Radical Equations”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg2.3.9 Lesson
- IM Alg2.3.9 Lesson: Solving Radical Equations
- Alg2.3.9 Practice
- IM Alg2.3.9 Practice: Solving Radical Equations
IM Alg2.3.9 Lesson: Solving Radical Equations
Solve these equations mentally:
[math]\sqrt[3]{x}=1[/math]
[math]\sqrt{7}=\sqrt{x-1}[/math]
[math]\sqrt{100}=2x[/math]
[math]\sqrt{x+1}=\text{-}5[/math]
Find the solution(s) to each of these equations, or explain why there is no solution.
[math]\sqrt{a-5}=5[/math]
[math]\sqrt[3]{a-5}=5[/math]
[math]\sqrt[3]{b}=\text{-}2[/math]
[math]\sqrt{c}+2=0[/math]
[math]\sqrt[3]{3-d}+4=0[/math]
[math]\sqrt{7}=\sqrt{x-1}[/math]
[math]\sqrt{36}=3y[/math]
[math]22z=\sqrt[3]{11}[/math]
Write an equation that includes a radical symbol with one solution.[br]
Write an equation that includes a radical symbol with no solutions.
Write an equation that includes a radical symbol with two solutions.[br]
Switch with a partner and solve their equations.
Find all solutions to the equation [math]\sqrt{x}=\sqrt[3]{x}[/math]. Explain how you know those are all of the solutions.
IM Alg2.3.9 Practice: Solving Radical Equations
Find the solution(s) to each of these equations, or explain why there is no solution.
[math]\sqrt{x+5}+7=10[/math]
[math]\sqrt{x-2}+3=\text{-}2[/math]
For each equation, decide how many solutions it has and explain how you know.
[math](x-4)^2=25[/math]
[math]\sqrt{x-4}=5[/math]
[math]x^3-7=\text{-}20[/math]
[math]6\cdot\sqrt[3]{x}=0[/math]
[size=150]Jada was solving the equation [math]\sqrt{6-x}=\text{-}16[/math]. She was about to square each side, but then she realized she could give an answer without doing any algebra. What did she realize?[/size]
[size=150]Here are the steps Tyler took to solve the equation [math]\sqrt{x+3}=\text{-}5[/math].[br][/size][br][math]\begin{align}\sqrt{x+3} &=-5\\x+3 &=25\\x &=22\end{align}[/math][br][br]Check Tyler’s answer: Is the equation true if [math]x=22[/math]? Explain or show your reasoning.[br]
What mistake did Tyler make?[br]
Complete the table. Use powers of 16 in the top row and radicals or rational numbers in the bottom row.
[size=150]Which are the solutions to the equation [math]x^3=35[/math]?[/size]