Beginning and Intermediate Algebra - Wallace Math Courses ...

If there is a binomial in the radical then we need to keep that binomial together
through the entire problem.
Example 424.
�
3x(y +z) 9x(y +z) 2
3
�
�
3x(y + z) 32x(y +z) 2
3
�
�
6
3 3 x 3 (y +z) 3 3 4 x 2 (y +z) 4
�
6
3 7 x 5 (y +z) 7
�
3(y +z) 3x5 6
(y + z)
Rewrite 9 as 3 2
Common index:6. Multiply first group by 3, second by 2
Add exponents, keep (y + z) as binomial
Simplify, dividing exponent by index, remainder inside
Our Solution
World View Note: Originally the radical was just a check mark with the rest of
the radical expression in parenthesis. In 1637 Rene Descartes was the first to put
a line over the entire radical expression.
The same process is used for dividing mixed index as with multiplying mixed
index. The only difference is our final answer cannot have a radical over the
denominator.
Example 425.
�
6
�
24
8
x 4 y 3 z 2
� Common index is 24. Multiply first group by 4, second by 3
x 7 y 2 z
x 16 y 12 z 8
x 21 y 6 z 3
x−5y6z 5
24 �
�
24
y 6 z 5
x 5
� ��
�
24
y 6 z 5
x 5
24
x 19
x 19
x19y6z5 24�
x
Subtract exponents
Negative exponent moves to denominator
Cannot have denominator in radical, need 12x ′ s, or7more
Multiply numerator and denominator by x7 12 √
Our Solution
316