roots

ROOTSFrom the 7th rule up to the 18th rule

Simplify the given expressions

1. =

Simplify the given expressions

4. =

5. =

Simplify the given expressions

7. =

8. =

Special Product

Examples

Examples (these are also called CONJUGATES)

Examples

6. .

7. .

Simplest Radical Form

1. NO fractions under .3. NO (Rationalzing denominator)

Simplest Radical Form

Conjugates Examples

Conjugates Examples

Conjugates Examples

Conjugates Examples

Homework

• Pg: 69

• Exercises between 61 and 74

Adding and Subtracting Radicals

• Radicals that have the same index and the same radicand are called like radicals.

• You can apply the distributive property to add/ subtract like radicals in the same way as like terms.

Combine like terms/ like radicals

•Like terms:• 5x+y-4x=

•Like radicals:

* First simplify each radical, then combine them if possible.

Examples (Add / Subtract)

Examples (Add / Subtract)

Examples (Add / Subtract)

Examples (Add / Subtract)

Examples (Add / Subtract)

Examples (Add / Subtract)

Homework

• Pg: 69

• Exercises between 47 and 60

Summary

•Write the rules that you know and use effectively.

•Support this rule with an example.•What you have learned up to this stage.

•What you have not learned or which parts of the subject is unclear to you.

Mixed Examples (Simplify)• * Assume that each radical represents a real number.

Mixed Examples (Simplify)• * Assume that each radical represents a real number.

Mixed Examples (Simplify)• * Assume that each radical represents a real number.

Mixed Examples (Simplify)• * Assume that each radical represents a real number.

•*

Mixed Examples (Simplify)• * Assume that each radical represents a real number.

•*

Mixed Examples (Simplify)• * Assume that each radical represents a real number.

Mixed Examples (Simplify)• * Assume that each radical represents a real number.

Rule 8:

Rule 8 (improved):

Rule 9: a (a is positive)

Rule 10:

Arrow Paradox of Zeno• In the arrow paradox, Zeno states that for motion to occur,

an object must change the position which it occupies.• He gives an example of an arrow in flight. He states that in

any one (durationless) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there.

• In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

...................................................................X

Rule 11 :

• Don’t use this rule, here is the method:

Rule 12:

• Be careful !!! It is finite with n radicals and it is square root.

Rule 13:

• You can use the method that I teach you

Rule 14:

• You can use the method that I teach you

Rule 15:

• You can use the method that I teach you

Rule 16:

• You will learn this method next year ;)

Rule 17:

• You will learn this method next year ;)

Rule 18:

Rule 18:

Rule 18:

All rules are covered! Mixed Exercises

Mixed Exercises

Mixed Exercises

• , find x

Mixed Exercises

• , find x

This is the end for this subject!