Week 5-Radical Equations

Aside

Add the square root of the same coefficient

ex: 1-3√5x=-3-2√5x

-3√5x+2√5x=-3-1

-√5x=-4

Than use the way that square both sides of this to get rid of the square root

5x=16

x=16/5

 

Review

\frac{2\sqrt{6}}{\sqrt{7}+\sqrt{5}}

[Than multiply both the top and the bottom by a number , which is goodfor removing the square root of the denominator((\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})=3-2=1)]

=\frac{2\sqrt{6}(\sqrt{7}-\sqrt{5})}{(\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5})}

=\frac{2\sqrt{42}-2\sqrt{30}}{7-5}

=\frac{2\sqrt{42}-2\sqrt{30}}{2}

=\sqrt{42}-\sqrt{30}

Week 4 -Adding and subtracting radical expressions

When you simplify your radicals down, you can only add common radicals together. When you’re adding or subtracting radicals, the radicand always stays the same, which is why you need to have a common radicand. Once you’ve collected common radicals you you either add or subtract the co-efficients together depending on the sign

EX:3√5+6√5(They have same radicand)=9√5

 

We also learned how to make it simplify

You have to simplify the number in the  root as much as you can by multiplying it by several equal numbers

EX:square root:√64=√4*4*4=4√4

cube root: ³ √81=³√3*3*3*3=3 ³√3

it makes you can better to add up some numbers with the root

 

 

see the picture

 

Week 3 Absolute Value and Radicals

√25=5

The absolute value of a real number is defined as the principal square root(√25) of the square of a number.

EX:|9|=3 ,|-9|=3

√9²=√81=9=|9|=|-9|

√(-9)²=√81=9=|9|=|-9|

Simplifying Radical Expressions

Coefficient√Radicand

Square roots :ex ²√16=4

Roots(-other roots)[

Cube roots :ex³√27=3

Warn:²√x     (x≥0)restriction

³√x     (x∈R)restriction

 

 

Week 2 Pre-calculus 11

 

Finite Geometric Series : you use this formula S_{n}=\frac{a(r^n -1)}{r-1}

Geometric Series : {

Infinite Geometric series : Because Diverging r>1 or r<-1,so no sum

For example : t=-0.5, r=-3

So -0.5,1.5,-4.5,13.5. It gets bigger and it gets smaller, no fixed size,either keep getting bigger or you keep getting smaller.

Converging: you can use this formula -1<r<1  S_{n}=a/1-r  n= ∞