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…