my answers to 3 radical problems.
- Thread starter SkitZoid
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What were the instructions for these various exercises?
How did you obtain your answers? For instance, for the fourth exercise, you have the square of a difference, so you started by writing out the square and then expanding (as you've been taught for things like "FOIL"):
. . . . .\(\displaystyle \left(\sqrt{6}\, -\, 3\right)^2\, =\, \left(\sqrt{6}\,-\, 3\right)\left(\sqrt{6}\,-\, 3\right)\)
. . . . . . . . . . . . . . .\(\displaystyle =\, \sqrt{6}\sqrt{6}\, -\, 3\sqrt{6}\, -\, 3\sqrt{6}\, +\, (3)(3)\)
How did you get from this to your final expression and value?
Please be complete. Thank you!
Eliz.
How did you obtain your answers? For instance, for the fourth exercise, you have the square of a difference, so you started by writing out the square and then expanding (as you've been taught for things like "FOIL"):
. . . . .\(\displaystyle \left(\sqrt{6}\, -\, 3\right)^2\, =\, \left(\sqrt{6}\,-\, 3\right)\left(\sqrt{6}\,-\, 3\right)\)
. . . . . . . . . . . . . . .\(\displaystyle =\, \sqrt{6}\sqrt{6}\, -\, 3\sqrt{6}\, -\, 3\sqrt{6}\, +\, (3)(3)\)
How did you get from this to your final expression and value?
Please be complete. Thank you!
Eliz.
SkitZoid said:
1) \(\displaystyle \frac{\sqrt{9}}{\sqrt{81}}=\frac{3}{9}=\frac{1}{3}\)
2) You may need to "rationalize" the denominator for this one. That means to eliminate the radical from the denominator. Eliminate the radical by multiplying both numerator and denominator by a value that makes the denominator an integer. It depends on what your instructions told you to do.
\(\displaystyle \frac{\sqrt[5]{1}}{\sqrt[5]{31}}=\frac{1}{\sqrt[5]{31}} \cdot \frac{(\sqrt[5]{31})^4}{( \sqrt[5]{31})^4}=\frac{\sqrt[5]{31^4}}{31}\)
3)Correct
Last one:
1)\(\displaystyle (\sqrt{6} - 3)^2\)
Use this rule: \(\displaystyle (a - b)^2=a^2-2ab+b^2\)
\(\displaystyle (\sqrt{6})^2-2(3\sqrt{6})+(3)^2\)
\(\displaystyle 6-6\sqrt{6}+9\)
\(\displaystyle 15-6\sqrt{6}\)
staple thanks for pointing out the explanations that are needed, next time I will do a better job explaining the steps and thought process along with the problems, that aught to help everyone involved
masters thanks for the explanation, much appreciated.
masters thanks for the explanation, much appreciated.