**RECALL:**

*Partial Fractions*! Read through the summaries posted by yourself/others

~(•o•)~ Level Tests are on Week 7 & 8, starting mugging.

**HOMEWORK:**

~(•o•)~ Check what you haven't done on the homework spreadsheet.

~(•o•)~ AceLearning for those who did badly on the various quizzes and tests.

~(•o•)~ Assignment 01 and 02 are now due on Friday~!

**REVISE:**

~(•o•)~ The 9 laws of indices: (here's a helpful table)

Please remember to fully revise all laws as they will be used in Indices and Surds.

**LESSON:**

~(•o•)~ Indices and Surds: Forms

Surd Form: When the base has a squareroot with it (√5)

Radical Form: When the base has an fractional index (2^(2/123))

~(•o•)~ Indices and Surds: Rationalization

*Rationalization is the act of eliminating the squareroot (√x) from the denominator.*

*BACK TO BASICS– " 1/2 VS 1/3"*

__How do we determine which is bigger?__

We change make them have an equal denominator. Thus, the LCM between 2 and 3 is 6. Therefore, we multiply 1/2 with 3/3 (Note how this is 1 whole), and 1/3 with 2/2. Eventually, we get "3/6 > 2/6"

ON TO SURDS! – "1/2 VS 1/√2"

__How do we determine which is bigger?__

Once again, we change them to make them have an equal denominator. In this case, we change the denominator to 2. As the first fraction already has a denominator of 2, we will work with 1/√2.

2 divided by √2 is √2. Thus, we multiply 1/√2 by √2/√2 (1 whole), and get √2/2.

Therefore, we would get "1/2 < √2/2"

Rationalizing with a^2 - b^2 – "1/(3 - 2) VS 1/(√3 - √2)"

To rid of the surd denominator, we use the 'a^2 b^2 = (a + b)(a - b)' concept.

In this scenario, our denominator is (√3 - √2) which is our (a - b). Thus, to rid of it, we multiply it by (√3 + √2) which represents our (a + b).

Thus, we multiply 1/(√3 - √2) by (√3 + √2)/(√3 - √2) <-- which is one whole!

This gives us (√3 + √2)/(3 - 2) = (√3 + √2)/1

Therefore, "1 < (√3 + √2)"

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