|
|
|
ALGEBRA
- solved problems
|
|
|
|
|
|
|
|
Radicals
(roots) and/or exponentiation
with fractional (rational) exponent
|
| Rules and properties of radicals
|
|
|
| 67. |
Find given roots or radicals.
|
|
| Solutions: |
a) |
 |
since
33
= 27. |
|
b) |
 |
since
(-3)3
= (-3)·(-3)·(-3)
= -
27. |
|
c) |
 |
since
(-2)5
= (-2)·(-2)·(-2)·(-2)·(-2)
= -32. |
|
| The odd root of any real number
exists. |
|
|
|
|
| Solutions: |
a) |
 |
since 42
= 16 and 4
> 0, [recall
that ( ±
4)2
= 16]. |
| |
b) |
 |
since 34
= 81 and 3
> 0, [recall
that ( ±
3)4
= 81]. |
|
|
The
even root of a nonnegative real number exists.
Note that the even root is defined to be a nonnegative
number.
|
|
The
even root of a negative real number does not exist as a real
number.
|
| For example, |
 |
do
not exist as real numbers, but they do exist as complex
numbers. |
|
|
| Rules and properties of radicals
and/or fractional exponents
|
|
|
If
m,
n and p
are natural numbers
(n
>1) and
if a
and b
are nonnegative
real numbers, then |
|
|
Properties |
|
Examples |
|
|
 |
|
 |
|
|
|
|
 |
|
|
 |
|
 |
|
|
 |
|
 |
|
|
 |
|
 |
|
|
 |
|
 |
|
|
 |
|
 |
|
|
 |
|
 |
|
|
|
|
Simplifying radical expressions
|
|
| 69. |
Simplify radical expressions.
|
|
|
|
|
|
Operations
on radical expressions |
| Adding, subtracting and multiplying
radicals
|
|
| 70. |
Solve given radical expressions.
|
|
| Solutions: |
 |
| |
 |
|
|
| 71. |
Solve given radical expressions.
|
|
|
|
|
| 72. |
Solve given radical expressions.
|
|
|
|
|
| 73. |
Solve given radical expressions.
|
|
|
|
|
| 74. |
Solve given radical expressions.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Solved
problems contents |
|
 |
|
| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
