6.6 Homework Problems: Radical Addition and Subtraction
1. Simplify the following radical expressions
a. [latex]\sqrt3\ +\ \sqrt5[/latex]
b. [latex]2\sqrt2\ +\ \sqrt2[/latex]
c. [latex]\sqrt{24}\ +\ \sqrt{48}[/latex]
d. [latex]3\sqrt6\ -\ 7\sqrt6[/latex]
e. [latex]\sqrt{20}+3\sqrt{80}-\ 19\sqrt5[/latex]
f. [latex]2\sqrt3\ -\ \sqrt{12}\ +\ 2\sqrt{18}[/latex]
g. [latex]3\sqrt{12}\ +\ 4\sqrt{48}\ -\ \sqrt{108}[/latex]
h. [latex]9\sqrt{12}\ +\ \sqrt{32}\ -\ \sqrt{72}[/latex]
2. Simplify the following radical expressions
a. [latex]3y\sqrt{3x^5}+x^2\sqrt{12xy^2}[/latex]
b. [latex]2w^2\sqrt{6{\rm wy}^5}\ -\ y\sqrt{96w^5}[/latex]
c. [latex]x\sqrt{54{\rm xw}^2}\ -\ 5w\sqrt{6x^3}[/latex]
d. [latex]8x\sqrt{48w^3}\ +\ w\sqrt{27{\rm wx}^2}[/latex]
e. [latex]-\sqrt[4]{32y^4}+\ 3\sqrt[4]{162y^8}[/latex]
f. [latex]-\sqrt[3]{32y^8}+\ 2\sqrt[3]{108y^8}[/latex]
3. Perform the requested operations and simplify as much as possible
a. [latex]\sqrt3\ (8\sqrt3\ -\ 2\sqrt6\ )[/latex]
b. [latex]\sqrt2\ (5\sqrt{10}\ +\ 2\sqrt2\ )[/latex]
c. [latex]2\sqrt5\ (3\sqrt{15}\ -\ 7\sqrt{10}\ )[/latex]
d. [latex]\ 3\sqrt7\ (9\sqrt{21}\ +\ 5\sqrt{14}\ )[/latex]
e. [latex](\sqrt5\ -\ \sqrt{x}\ )(\sqrt5\ +\ \sqrt{x}\ )[/latex]
f. [latex](2\sqrt5\ -\ 3\sqrt{2x}\ )(2\sqrt5\ +\ 3\sqrt{2x}\ )[/latex]
g. [latex]{\ (3\sqrt{x}\ +\ \sqrt5\ )}^2[/latex]
h. [latex]{\ (4\sqrt{w}\ -\ 2\sqrt5\ )}^2[/latex]