Division Property of Square and Cube Roots
It is often useful to write a single radical that contains a fraction as the
quotient of two radicals, and vice versa.
|
Property —The Division Property of Square Roots and
The Division Property of Cube Roots
English The root of a quotient is the quotient of the roots. |
| |
Square Roots |
Cube Roots |
| Algebra |
 |
 |
| Example |
Here, a and b are
nonnegative real numbers and b ≠ 0.
 |
Here, a and b are
real numbers and b ≠ 0.
 |
This property allows us to write a single radical as the quotient of two
radicals.
For example,
The property can also be used to write the quotient of two radicals as a
single radical, provided the radicals have the same index.
For example,
Note:
The Division Property applies only when
the indices of the radicals are the same. So
we cannot use it to divide a square root by
a cube root.
That is, we cannot use the Division
Property to find
 .
|