Respuesta :
To multiply radical expressions with the same index, we use the product rule for radicals. [tex]\sqrt[n]{A}.\sqrt[n]{B} = \sqrt[n]{A.B}[/tex]
To divide radical expressions with the same index, we use the quotient rule for radicals. [tex]\frac{\sqrt[n]{A} }{\sqrt[n]{B} } =\sqrt[n]{\frac{A}{B} }[/tex]
Multiplying Radical Expressions :
Example,
given: Multiply: [tex]\sqrt[3]{12} .\sqrt[3]{6}[/tex]
Apply the product rule for radicals, and then simplify.
[tex]\sqrt[3]{12}.\sqrt[3]{6}=\sqrt[3]{12.6}[/tex]
[tex]=\sqrt[3]{72}\\=\sqrt[3]{2^{3} .3^{2} } \\=2\sqrt[3]{3^{2} } \\=2\sqrt[3]{9}[/tex]
Dividing Radical Expressions
Example,
given: Divide: [tex]\frac{\sqrt[3]{96} }{\sqrt[3]{6} }[/tex]
In this case, we can see that 6 and 96 have common factors. If we apply the quotient rule for radicals and write it as a single cube root, we will be able to reduce the fractional radicand.
[tex]\frac{\sqrt[3]{96} }{\sqrt[3]{6} } =\sqrt[3]{\frac{96}{6} }[/tex]
[tex]=\sqrt[3]{16} \\=\sqrt[3]{8.2} \\=2\sqrt[3]{2}[/tex]
To learn more about fractional radicand, visit
brainly.com/question/1542580
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