Unit 6.5 Multiplying and Dividing Radical Expressions
Multiplying Radical Expressions
Product Rule
[latex]\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}[/latex]
(only if they are the same root!)
Distributive Property and FOIL Method
[latex](\sqrt{a} + \sqrt{b})(\sqrt{c} + \sqrt{d}) = \sqrt{a}\sqrt{c} + \sqrt{a}\sqrt{d} + \sqrt{b}\sqrt{c} + \sqrt{b}\sqrt{d}[/latex]
Multiplying Radical Expressions
[latex]\sqrt{5x} \cdot \sqrt{20x^3} = \sqrt{(5x) \cdot (20x^3)} = \sqrt{100x^4} = 10x^2[/latex]
FOIL Method
Multiply [latex](\sqrt{3} + \sqrt{2})(\sqrt{5} + \sqrt{7})[/latex]
[latex]= \sqrt{3}\sqrt{5} + \sqrt{3}\sqrt{7} + \sqrt{2}\sqrt{5} + \sqrt{2}\sqrt{7}[/latex]
[latex]= \sqrt{15} + \sqrt{21} + \sqrt{10} + \sqrt{14}[/latex]
Dividing Radical Expressions
Quotient Rule
[latex]\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}, \quad b \neq 0[/latex]
Dividing Radical Expressions
Divide [latex]\frac{\sqrt{50x^3}}{\sqrt{2x}}[/latex]
[latex]\frac{\sqrt{50x^3}}{\sqrt{2x}} = \sqrt{\frac{50x^3}{2x}} = \sqrt{25x^2} = 5x[/latex]