**√8**

= √4 x 2

= 2√2

**√75**

= √25 x 3

= 5√3

**Remember: If you can**

Some more examples we did in class:

*do*it, you can*undo*it.**5√48 + 2√75**

*First change the radicands into like terms*.

**5√16 x 3**

= 5√4(4) x 3

= 5(4)√3

= 20√3

**2√25 x 3**

= 2√5(5) x 3

= 2(5)√3

= 10√3

*Simplify by adding the like terms.*

**20√3 + 10√3**

= 30√3

= 30√3

**Next example:**

They are like terms, they can be added. Do not add radicands; they remain the same.

**2√5 – 9√5**

**= - 7√5**

Mr. Kuropatwa gave us yet another equation to try. There were two people who showed heir work to the class: Faven and Yassin.

**(2√5 – 3)(√5 + 1)**

= 2√5 + 2√5 – 3√5 – 3

= 4√5 – 3√5 – 3

= 2√5 + 2√5 – 3√5 – 3

= 4√5 – 3√5 – 3

**= √5 – 3**

**= 2√25 + 2√5 – 3√5 – 3**

**= 10 – √5 – 3**

**= 7 – √5**

E.g.

E.g.

**_**

√3

__2___√3

√3 is an

*irrational*number.

2 is a

*rational*number.

_

√3

_

__2___√3

**T**

*his is a rational number because it is a fraction. It is also an irrational number because the denominator is irrational.*

Mr. Kuropatwa told us that the Pythagorean Theorem was not created by Pythagorus himself but by one of his students, who has remained unknown. Apparently, you cannot measure the “c” side of a right triangle because they prefer that each side is to be made as only a unit of 1. It is impossible because:

**1² + 1² = c²**

1 + 1 = c²

√2 = √c²

√2 = c

It is impossible to measure because √2 equals an infinite decimal; it is and irrational number.

Then, we talked about the difference of squares for review.

For example:

**x² - 4**

= (x + 2 ) ( x – 2 )

= x² – 2x + 2x – 4

= x² - 4

At the end, Mr. Kuropatwa gave us a unit review. Pre Test will be tomorrow.

The next scribe will be Kris

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