[Week 4]- Multiplying and Dividing Radical Expressions

What I have learned:

- Adding and Subtracting Radical Expressions
- Simplifying with more than one set of like terms
- Multiplying and dividing radical expressions
- simplifying products of expressions with variable radicands
- Rationalizing a monomial denominator

Ex. Simplify √63+√40-√90-√28

The radicals are different, so simplify each radical.

√63+√40-√90-√28

= 3√7+2√10-3√10-2√7

= 3√7-2√7+2√10-3√10

= √7-√10

Ex. Simplify 2√x-3√y+5√x+2√y; x,y,≥0

2√x and 5√x are like terms because they are radicand x and index 2.

3√y and 2√y are like terms because they have radical y and index 2.

2√x-3√y+5√x+2√y

= 2√x+5√x-3√y+2√y

= 7√x-√y

Ex. Expand and simplify(2√3+5)(2√3-5)

Expand

(2√3+5)(2√3-5)

= (2√3)(2√3)-5*5

= 12- 25

= -13

[Week 3]- Absolute value of a real number

What I have learned:

- What is the absolute value of a real number
- The absolute value of a real number is defined as the principal square root if the square of a number.
- Determine absolute value.
- The relationship with absolute and principal square root.
- √x ² = |x|

Ex. Determine each absolute value.

|4.2|, |-6.1|, |0|, | -3/4 |

4.2, 6.1, 0, 3/4

^{ }

Ex. Evaluate√（3-5） ^{2}

^{ }Use the fact that √（3-5）^{2 } = |x|

√（3-5）^{2 }= |3-5|

^{ } = |-2|

= 2

[Week 2]- Geometric Series

What I have learned:

- The sum of n terms of a geometric series
- Use a rule to determine the sum of n terms of a geometric series, then solve related problems.
- Use a rule to determine the nth term in a geometric sequence.
- Use a rule to determine any of n, t1, tn, or r in a geometric sequence.
- Use a rule to determine n and Sn in geometric series, given the values of r, n, or Sn.

Ex. Find the S15 of the sequence -5, 10, -20…

Ex. Find the n of the sequence 1-2+4-8+…-512

[Week 1]- Arithmetic Sequences

What I have learned:

- what is arithmetic sequences and common different.
- How to find common different.
- How to calculate the sum of n term of an arithmetic series
- Use a rule to determine t1 and d in an arithmetic sequence given the values of tn and n.
- Use a rule to determine tn and n in an arithmetic sequence given the values of t1 and d.
- Use a rule to determine the sum Sn of an arithmetic series.

Ex. Use the arithmetic series, determine the indicated value.

1 + 3.5 + 6 + 8.5 + …; determine S42.

Know: Sn = n/2 [2 t1 + d (n-1)]

T1 = 1 = 42/2[2+2.5*41]

T2= 3.5 = 2194.5

d= 2.5

Ex. Use the giving data to determine the indicated value.

S20 = -850 and t20 = -90; determine t1

Sn = n/2 (t1 +tn)

-850 = 20/2[t1 +(-90)]

10 t1 = 50

t 1 = 5

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