Chapter 4 Pre-Requisite Skills

Goals:

• Finding the Trig Buttons

• Simplifying Roots

• Rationalizing Roots

• Pythagorean Theorem

​

​Review of some

old stuff to get ready for next stuff...

​These slides go directly along with the Worksheet I gave you!

Copy all the examples down on the worksheet, and try out the "You Try" problems!

Find the "sin" , "cos", and "tan" buttons...

• If no actual buttons, look for a "TRIG" screen

• Could be actual button or above a button

• Raise hand/ask a friend for help if you can't find

​​Goal 1:

Find the trig buttons on your calculator...

​​Test it out: Try finding "sin(60)" and confirm you get 0.8660

Raise your hand if you don't get this before moving on.

If you got -0.3048:

* You are in RADIAN mode.

* You need to be in DEGREE mode

* You may see an "R" or "RAD" on your screen

* You have to find a mode button or similar and look for "deg" or "drg" and try again.

​​If you did NOT get the right answer:

Multiple Choice

Find $$\cos\left(23\degree\right)$$

Raise your hand/ask for help if you do not get it right!

• 0.9205

• 0.3907

• -0.8462

• 0.6469

Multiple Choice

Find $$\tan\left(47\degree\right)$$

If you STILL do not get it right, make a note to ask me tomorrow!.

• -0.1245

• 0.1236

• 0.7314

• 1.0724

A square root is not "simplified" if the number inside contains any perfect square factors.

​​Goal 2:

Simplifying Roots

• Look to the table of perfect squares to the left.

• You should commit as many of these to memory as you can.

​​Goal 2:Simplifying Roots (Ex 1)

​​Goal 2: Simplifying Roots (Ex 2)

​​Goal 2: Simplifying Roots (Ex 3)

​​Goal 2: Simplifying Roots (Ex 4)

Multiple Choice

Simplify the root completely:

$$7\ \sqrt[]{200}$$

CHECK ANSWER EXPLANATION if you do not get it correct!

• $$14\ \sqrt[]{10}$$

• $$70\ \sqrt[]{2}$$

• $$700\ \sqrt[]{2}$$

• cannot be simplified

Multiple Choice

Simplify the root completely:

$$\frac{\sqrt[]{50}}{10}$$

Check answer explanation if you do not get it correct!

• $$5$$

• $$\frac{\sqrt[]{2}}{2}$$

• $$\frac{\sqrt[]{5}}{5}$$

• $$\frac{\sqrt[]{10}}{2}$$

Multiple Choice

Simplify the root completely:

$$3\ \sqrt[]{70}$$

Check answer explanation if you do not get it correct!

• $$21\ \sqrt[]{10}$$

• $$30\ \sqrt[]{7}$$

• $$6\sqrt[]{35}$$

• cannot be simplified

We do not like roots in denominators, so if there ever IS a root in a denominator, we try to "rationalize" it.

​​Goal 3:

Rationalizing Roots

​​Goal 2: Rationalizing Roots (Ex 1 and Ex 2)

​​Goal 2: Rationalizing Roots (Ex 3)

​​Goal 2: Rationalizing Roots (Ex 3)

Multiple Choice

Rationalize and simplify:

$$\frac{5}{\sqrt[]{2}}\$$

Check answer explanation!!!

• $$\ \frac{5\ \sqrt[]{2}}{2}$$

• $$\frac{\sqrt[]{10}}{2}$$

• $$2\ \sqrt[]{5}$$

• $$5\ \sqrt[]{2}$$

Multiple Choice

Rationalize and simplify:

$$\frac{3}{2\ \sqrt[]{5}}\$$

Check answer explanation!!!

• $$\ \frac{3\ \sqrt[]{5}}{2}$$

• $$\frac{3\sqrt[]{5}}{10}$$

• $$\ \frac{3\ \sqrt[]{5}}{50}$$

• $$3\ \sqrt[]{5}$$

Multiple Choice

Rationalize and simplify:

$$\frac{\sqrt[]{7}}{\sqrt[]{6}}\$$

Check answer explanation!!!

• $$\ \ \sqrt[]{42}$$

• $$\frac{6\sqrt[]{7}}{7}$$

• $$\ \frac{\sqrt[]{42}}{36}$$

• $$\frac{\sqrt[]{42}}{6}$$

You know it... let's make sure you can USE it!

​​Goal 4:

Pythagorean Theorem

​​Goal 2:

Pythagorean Theorem (Ex 1)

​​Goal 2:

Pythagorean Theorem (Ex 2)

​​Goal 2:

Pythagorean Theorem (Ex 3)

Multiple Choice

Find x.

Simplify completely.

Leave exact. No decimals.

• none of these

• $$2\ \sqrt[]{3}$$

• $$\sqrt[]{12}$$

• 10

Multiple Choice

Find x.

Simplify completely.

Leave exact. No decimals.

• $$\sqrt[]{125}$$

• $$3\ \sqrt[]{5}$$

• $$5\ \sqrt[]{3}$$

• $$5\ \sqrt[]{5}$$

Multiple Choice

Find x.

Simplify completely.

Leave exact. No decimals.

• $$2\ \sqrt[]{5}$$

• $$5\ \sqrt[]{2}$$

• $$2\ \sqrt[]{14}$$

• $$4\ \sqrt[]{5}$$