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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]

 

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