7.3 binomial radical expressions. review example
DESCRIPTION
RADICAL EXPRESSIONS EX-adding RULES –Have to have same number on inside –Have to have same nth rootTRANSCRIPT
7.3 Binomial Radical Expressions
Review Example
521
2
az8z5
5
22
1
az8z5
521az8
5
5 342
5 342
az2
az2
5 555
5 34
az2
az20
az2az205 34
RADICAL EXPRESSIONSEX-adding
• RULES– Have to have
same number on inside
– Have to have same nth root
482273122
3162393342
342333322
383934
321
RADICAL EXPRESSIONSEX-adding
333 128544163
3 73 33 4 223423
3 63 33 3 22234223
3233 22234223
333 2421226 3 22
Let’s try some . . .
7238418
3 832350
Solutions
7238418
3 832350
Review - RATIONALIZING a DENOMINATOR
• How to rationalize using conjugates– If there is a radical in the bottom, then you
must rationalize it.
25
22
2
25
How to rationalize when there are rationals in the denominator…
32a2
53 2
3 2
a2
a2
3 33
3
a2
a20
a2a203
Multiply by the same root but make it so youcan take root of the powers
Let’s remember conjugates
?)5 (2 of conjugate theisWhat )52(
)342(
44484
Sample: Find the conjugate of
Multiply the binomial by the conjugate using the box method.
2
4
16(3)=-48)34
34 2
)38
)38
Notice: No roots appear in our solution when we multiply by a conjugate
RADICAL EXPRESSIONS EX-FOIL Method
)32)(3253(
56 153 34 6+ - -
Fully simplified since radicals can’t break downand our addition rules don’t apply
EX-rationalizing
3531
3535
335352533535
22368
11
334
CONJUGATE