Algebra II Honors Problem of the Day Homework: p. 33 9 – 11 all, 33-41 all

Algebra II Honors Problem of the DayHomework: p. 33 9 – 11 all, 33-41 all

Given that x is a member of the set of real numbers,name all x that satisfy each of the following equations.

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a) x2 =16

b) x2 = −16

c) x3 = 8

d) x3 = −8

e) x2 = 0

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a) ± 4

b) no real ans.

c) 2

d) − 2

e) 0

Principal Roots for Radicals

When a radical has an even index there are two possible solutions. One positive and one negative.

When a radical has an odd index there is only one possible solution.

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32 = 9 −3( )2 = 9

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23 = 8 −2( )3 = −8

Use absolute value symbols on variables when simplifying radical expressions if:

The radical has an even index and the variable that is in the solution has an odd exponent.

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x8

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x6

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x155

Algebra II Honors Problem of the DayHomework: p. 33 12, 23-32 all 61-65 all

Simplify the following:

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−3x4y5

3−3 x−2y16

⎛

⎝ ⎜

⎞

⎠ ⎟

−2

Rules for Simplifying Radicals

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abn = an ⋅ bn (note: if n is even, ab must be positive so that an answer is possible)

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54x4y5 =

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=3x2y2 6y

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32 ⋅ 6 ⋅ x4 ⋅ y4 ⋅ y

You might not need to write all of the steps out. Keep in mind you are trying to make sure you don’t leave perfect nth roots inside the radical.

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96x5y43 =

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=2xy 12x2y3

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23 ⋅22 ⋅3⋅x3x2y3y3

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a

bn =

an

bn

A rule similar to the first one applies to fractions.

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502

=502

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=5

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= 25

Reduce fractions before simplifying.€

5x5

643 =

5x53

643

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=x 5x23

4

Do the parts individually if the fraction doesn’t reduce

No radicals are allowed in the denominator.

Rationalizing the denominator:

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1

arn

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⋅ asn

asn

where r + s = n