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- Radicals

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

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Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

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Get Started Now- Intro Lesson16:11
- Lesson: 1a0:22
- Lesson: 1b1:00
- Lesson: 1c2:56
- Lesson: 1d0:28
- Lesson: 1e3:34
- Lesson: 2a6:43
- Lesson: 2b4:28
- Lesson: 2c5:42
- Lesson: 2d2:48
- Lesson: 2e5:58
- Lesson: 2f2:41
- Lesson: 318:21
- Lesson: 4a0:55
- Lesson: 4b0:37
- Lesson: 4c3:29
- Lesson: 4d1:57

Related concepts: Basic radical functions, Transformations of radical functions, Square root of a function, Solving radical equations,

$\cdot$ 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. ${^3}\sqrt{-64}=-4$

${^{even}}\sqrt{negative}=undefined$ i.e. $\sqrt{-64}=undefined$

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

i.e. ${^3}\sqrt{-64}=-4$

- Introduction$\cdot$What is a “radical”?

$\cdot$square root VS. cubic root

$\cdot$commom squares to memorize

- 1.
**Evaluating Radicals Algebraically**

Without using a calculator, evaluate:a)$\sqrt { - 9}$b)${^3}\sqrt{{ - 27}}$c)${^6}\sqrt{{\frac{1}{{64}}}}$d)${^4}\sqrt{{ - 81}}$e)$9{^3}\sqrt{{64}}$ - 2.
**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)$\frac{3}{4}{^4}\sqrt{{36}}$ - 3.
**Radical Rules**

Combining radicals: Do's and Don'ts - 4.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)${^3}\sqrt{5} \cdot {^3}\sqrt{{25}} = 5$

5.

Radicals

5.1

Square and square roots

5.2

Cubic and cube roots

5.3

Evaluating and simplifying radicals

5.4

Converting radicals to mixed radicals

5.5

Converting radicals to entire radicals

5.6

Adding and subtracting radicals

5.7

Multiplying and dividing radicals

5.8

Rationalize the denominator

5.9

Operations with radicals

5.10

Conversion between entire radicals and mixed radicals

5.11

Adding and subtracting radicals

5.12

Multiplying radicals (advanced)

5.13

Solving radical equations (advanced)

We have over 1420 practice questions in College Algebra for you to master.

Get Started Now5.1

Square and square roots

5.2

Cubic and cube roots

5.3

Evaluating and simplifying radicals

5.4

Converting radicals to mixed radicals

5.5

Converting radicals to entire radicals

5.6

Adding and subtracting radicals

5.7

Multiplying and dividing radicals

5.8

Rationalize the denominator

5.9

Operations with radicals

5.10

Conversion between entire radicals and mixed radicals

5.11

Adding and subtracting radicals

5.12

Multiplying radicals (advanced)