# Operations with radicals

### Operations with radicals

#### Lessons

$\cdot$ 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. ${^3}\sqrt{-64}=-4$
• 1.
$\cdot$What is a “radical”?
$\cdot$square root VS. cubic root
$\cdot$commom squares to memorize

• 2.
Without using a calculator, evaluate:
a)
$\sqrt { - 9}$

b)
${^3}\sqrt{{ - 27}}$

c)
${^6}\sqrt{{\frac{1}{{64}}}}$

d)
${^4}\sqrt{{ - 81}}$

e)
$9{^3}\sqrt{{64}}$

• 3.
Evaluating Radicals Using a Calculator
Use a calculator to determine:
a)
${\;}{^6}\sqrt{{729}}$

b)
${^5}\sqrt{{-1024}}$

c)
${^5}\sqrt{{\frac{{32}}{{243}}}}$

d)
${^6}\sqrt{{600}}$

e)
${^5}\sqrt{{0.5}}$

f)
$\frac{3}{4}{^4}\sqrt{{36}}$

• 4.
Combining radicals: Do's and Don'ts

• 5.
Determine whether the following statements are true or false.
a)
$\sqrt 2 \times \sqrt 3 = \sqrt 6$

b)
$\frac{{\sqrt {20} }}{{\sqrt {10} }} = \sqrt 2$

c)
$\sqrt {15} \cdot\sqrt {30} \cdot\sqrt 2 = 900$

d)
${^3}\sqrt{5} \cdot {^3}\sqrt{{25}} = 5$