Properties Of Radicals, Simplifying Radicals, Rationalizing Operations Worksheet

Properties Of Radicals, Simplifying Radicals, Rationalizing Operations Worksheet - Section A-7

A-57

A-7 Radicals

Section A-7 Radicals

From Rational Exponents to Radicals, and Vice Versa

Properties of Radicals

Simplifying Radicals

Sums and Differences

Products

Rationalizing Operations

What do the following algebraic expressions have in common?

1/2

2/3

1/2

Each vertical pair represents the same quantity, one in rational exponent form and

the other in radical form. There are occasions when it is more convenient to work

with radicals than with rational exponents, or vice versa. In this section we see

how the two forms are related and investigate some basic operations on radicals.

From Rational Exponents to Radicals, and Vice Versa

We start this discussion by deﬁning an nth-root radical.

, nTH-ROOT RADICAL

D E F I N I T I O N

For n a natural number greater than 1 and b a real number, we deﬁne

to be the principal nth root of b (see Deﬁnition 2 in Section A-6);

that is,

1/n

If n

2, we write

in place of

1/2

1/5

1/2

1/5

( 32)

1/4

is not real.

The symbol

is called a radical, n is called the index, and b is called the

radicand.

As stated above, it is often an advantage to be able to shift back and forth

between rational exponent forms and radical forms. The following relationships,

which are direct consequences of Deﬁnition 1 and Theorem 2 in Section A-6, are

useful in this regard:

Properties Of Radicals, Simplifying Radicals, Rationalizing Operations Worksheet - Section A-7