# Operations with radicals

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##### Intros
###### Lessons
1. $\cdot$What is a "radical"?
$\cdot$square root VS. cubic root
$\cdot$common squares to memorize
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##### Examples
###### Lessons
1. Evaluating Radicals Algebraically
Without using a calculator, evaluate:
1. $\sqrt { - 9}$
2. ${^3}\sqrt{{ - 27}}$
3. ${^6}\sqrt{{\frac{1}{{64}}}}$
4. ${^4}\sqrt{{ - 81}}$
5. $9{^3}\sqrt{{64}}$
2. Evaluating Radicals Using a Calculator
Use a calculator to determine:
1. ${\;}{^6}\sqrt{{729}}$
2. ${^5}\sqrt{{-1024}}$
3. ${^5}\sqrt{{\frac{{32}}{{243}}}}$
4. ${^6}\sqrt{{600}}$
5. ${^5}\sqrt{{0.5}}$
6. $\frac{3}{4}{^4}\sqrt{{36}}$
3. Radical Rules
Combining radicals: Do's and Don'ts
1. Determine whether the following statements are true or false.
1. $\sqrt 2 \times \sqrt 3 = \sqrt 6$
2. $\frac{{\sqrt {20} }}{{\sqrt {10} }} = \sqrt 2$
3. $\sqrt {15} \cdot\sqrt {30} \cdot\sqrt 2 = 900$
4. ${^3}\sqrt{5} \cdot {^3}\sqrt{{25}} = 5$
###### Topic Notes
$\cdot$ even root: ${^{even}}\sqrt{positive}=defined$
i.e. $\sqrt{64}=8$
${^{even}}\sqrt{negative}=undefined$
i.e. $\sqrt{-64}=undefined$

$\cdot$ odd root: ${^{odd}}\sqrt{positive\;or\;negative}=defined$
i.e. ${^3}\sqrt{64}=4$
i.e. ${^3}\sqrt{-64}=-4$