spacewater
Junior Member
- Joined
- Jul 10, 2009
- Messages
- 67
problem : 16 over 16 cube root
\(\displaystyle \frac{16}{^3\sqrt{16}}\)
steps
\(\displaystyle \frac{16 \cdot ^3\sqrt{16}}{^3\sqrt{16} \cdot ^3\sqrt{16}}\)
\(\displaystyle \frac{16 \cdot ^3\sqrt{16}}{16}\)
Cancel out 16 on the numerator and the denominator
the final answer
\(\displaystyle 2\cdot^3\sqrt{2}\)
my final answer does not correspond with the answersheet. I believe i did everything right so i am seeking for help.
problem 2: 6 over 1 minus 3 square root
\(\displaystyle \frac{6}{1 - \sqrt{3}}\)
steps
\(\displaystyle \frac {6\cdot 1+\sqrt{3}}{1-\sqrt{3}\cdot 1+\sqrt{3}}\)
\(\displaystyle \frac{6+6\sqrt{3}}{1-3}\)
final answer
\(\displaystyle -\frac{6-6\sqrt{3}}{2}\)
Shouldn't this be the final answer since you cant cancel out the numerator and denominator due to the subtraction between \(\displaystyle 6\) and \(\displaystyle 6\sqrt{3}\)? I thought only the one with either multiplication/division can cancel out when it comes to fraction.
For example
\(\displaystyle \frac{6+x}{2x}\)
2 and 6 shouldn't cancel out since there is an addition going on in the numerator.
\(\displaystyle \frac{16}{^3\sqrt{16}}\)
steps
\(\displaystyle \frac{16 \cdot ^3\sqrt{16}}{^3\sqrt{16} \cdot ^3\sqrt{16}}\)
\(\displaystyle \frac{16 \cdot ^3\sqrt{16}}{16}\)
Cancel out 16 on the numerator and the denominator
the final answer
\(\displaystyle 2\cdot^3\sqrt{2}\)
my final answer does not correspond with the answersheet. I believe i did everything right so i am seeking for help.
problem 2: 6 over 1 minus 3 square root
\(\displaystyle \frac{6}{1 - \sqrt{3}}\)
steps
\(\displaystyle \frac {6\cdot 1+\sqrt{3}}{1-\sqrt{3}\cdot 1+\sqrt{3}}\)
\(\displaystyle \frac{6+6\sqrt{3}}{1-3}\)
final answer
\(\displaystyle -\frac{6-6\sqrt{3}}{2}\)
Shouldn't this be the final answer since you cant cancel out the numerator and denominator due to the subtraction between \(\displaystyle 6\) and \(\displaystyle 6\sqrt{3}\)? I thought only the one with either multiplication/division can cancel out when it comes to fraction.
For example
\(\displaystyle \frac{6+x}{2x}\)
2 and 6 shouldn't cancel out since there is an addition going on in the numerator.