radicals
Post on 12-Nov-2014
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n k
RADICALS
The nth root of a number k is a number r which, when raised to the power of n, equals k
r
RADICALS
rn kSo,
means that
rn=k
Rational exponents
nm
n m aa
Rational exponents
mnnm
n m aaa Notice that when you are dealing with a radical expression, you can convert it to an expression containing a rational (fractional) power. This conversion may make the problem easier to solve.
Properties of Radicalsnnp p aa
nnn baba
n
n
n
b
aba
n Ppn aa nmmn aa
Properties of Radicals
nnp p aa
nn1
npp
np p aa)gsimplifyin(aa
Properties of Radicals
nnn1
n1
n1
n baba)ba(ba
nnn baba
Properties of Radicals
n
n
n1
n1
n1
n
b
a
b
aba
ba
n
n
n
b
aba
Properties of Radicals
n Pnp
pn1p
n1
pn aaaaa
n Ppn aa
Properties of Radicals
nmmn1
m1
n1m
1
n1
mn1
mn aaaaaa
nmmn aa
Rationalizing Denominators with Radicals
7
2
You should never leave a radical in the denominator of a fraction.
Always rationalize the denominator.Example 1 (monomial denominator)
Rationalize the following expression:
772
7
7
7
2
7
2 Answer:
Rationalizing Denominators with Radicals
7 9
4
You should never leave a radical in the denominator of a fraction.
Always rationalize the denominator.
Example 2 (monomial denominator)
Rationalize the following expression:
734
3
34
33
34
3
3
3
4
3
4
9
4 7 5
7 7
7 5
7 52
7 5
7 5
7 5
7 27 27
Answer:
Rationalizing Denominators with Radicals
35
2
You should never leave a radical in the denominator of a fraction.
Always rationalize the denominator.
Example 3 (binomial denominator)
Rationalize the following expression:
22
352325352
35
352
35
35
35
2
35
222
Answer:
You will need to multiply the numerator and denominator by the denominator's conjugate
Exercises Now, you can practice doing exercises on your own…
THE MORE YOU PRACTICE, THE MORE YOU LEARN
…and remember…
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