Basic Technical Mathematics, 11th Edition

11.5 Multiplication and Division of Radicals

• Multiplication of Radicals • Power of a Radical • Division of Radicals • Rationalizing the Denominator

When multiplying expressions containing radicals, we use the equation $\sqrt[n]{a}\sqrt[n]{n}\hspace{0.17em}=\hspace{0.17em}\sqrt[n]{ab}\hspace{0.17em},\hspace{0.17em}$ along with the normal procedures of algebraic multiplication. Note that the product of two radicals can be combined only if the orders of the radicals are the same. The following examples illustrate the method.

EXAMPLE 1 Multiplying monomial radicals

1. $\sqrt{5}\sqrt{2}\hspace{0.17em}=\hspace{0.17em}\sqrt{5\hspace{0.17em}\times \hspace{0.17em}2}\hspace{0.17em}=\hspace{0.17em}\sqrt{10}$

2. 

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   Note that we express the resulting radical in simplest form.

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Practice Exercise

1. Multiply: ...