6.4 Homework Problems: Simplifying Radical Expressions with Variables
1. Simplify the radical
a. [latex]\sqrt{x^6}[/latex]
b. [latex]\sqrt{a^{12}}[/latex]
c. [latex]\ \sqrt{y^{32}}[/latex]
d. [latex]\sqrt{4y^2}[/latex]
e. [latex]\sqrt{36x^{16}}[/latex]
f. [latex]\sqrt{121b^{44}}[/latex]
2. Simplify the radical
a. [latex]\sqrt{{108x}^7}[/latex]
b. [latex]\sqrt{196x^5}[/latex]
c. [latex]\sqrt{{294x}^{11}}[/latex]
d. [latex]\sqrt{525y^{33}}[/latex]
3. Find the nth root of the polynomial
a. [latex]\sqrt[3]{27x^6}[/latex]
b. [latex]\sqrt[4]{16y^{32}}[/latex]
c. [latex]\sqrt[6]{64a^{18}}[/latex]
d. [latex]\sqrt[5]{96x^6}[/latex]
e. [latex]\sqrt[3]{108x^6}[/latex]
f. [latex]\sqrt[4]{144y^9}[/latex]
g. [latex]\sqrt[7]{10935w^{81}}[/latex]
4. Simplify the radical, write in simplest terms
a. [latex]\sqrt{{99x}^4y^9}[/latex]
b. [latex]\ \sqrt{63ab^7}[/latex]
c. [latex]\sqrt{252x^{12}y^{15}}[/latex]
d. [latex]\sqrt{150x^3y^5}[/latex]
e. [latex]\sqrt[3]{72x^{11}w^9}[/latex]
f. [latex]\sqrt[3]{54t^{14}y^3}[/latex]
5. Simplify the radical expression by using absolute value signs where required
a. [latex]\sqrt{x^{6}y^{8}}[/latex]
b. [latex]\sqrt[4]{x^{16}y^{28}}[/latex]
c. [latex]\sqrt[2]{{36x}^2y^6}[/latex]
d. [latex]\sqrt[4]{{81x}^{12}y^8}[/latex]
Unit 6.4 Homework Printable Copy