6.5 Homework Problems: Multiplying and Dividing Radical Expressions

1. Multiply the radical expressions

a. [latex]\sqrt{15}\ \cdot\ \sqrt{15}[/latex]

b. [latex]\sqrt2\ \cdot\ \sqrt{32}[/latex]

c. [latex]4\sqrt{20}\ \cdot\ \sqrt{48}[/latex]

d. [latex]3\sqrt2\ \cdot\ 2\sqrt6[/latex]

2. Multiply the radical expressions and simplify as much as possible

a. [latex]\sqrt{5x}\ \cdot\ \sqrt{15x}[/latex]

b. [latex]\sqrt{2x^3y^4}\ \cdot\ \sqrt{10xy^3}[/latex]

c. [latex]\sqrt{6ab^5}\ \cdot\ \sqrt{30a^3b^3}[/latex]

d. [latex]\sqrt{18w^3v^5}\ \cdot\ \sqrt{3v^2w^2}[/latex]

3. Divide the radical expression and simplify as much as possible

a. [latex]\frac{\sqrt{72y^3}}{\sqrt{49y^6}}[/latex]

b. [latex]\frac{\sqrt{45w^4}}{\sqrt{9w^2}}[/latex]

4. Perform the requested operation and simplify as much as possible

a. [latex]\sqrt[6]{w}\cdot\ \sqrt[4]{w^3}[/latex]

b. [latex]\ \frac{\sqrt[5]{a^6}}{\sqrt[2]{a}}[/latex]

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