intermediate algebra

[Vhull]

I need help solving this: rationalize the demoninator

square root of x +2 (the +2 is not under the square root of x
divided by 3- square root of x


also question on this: use rational exponents to write a single radical expression. Assume that all variables represent nonnegative numbers.

index 3 square root 3y^2 times index 4 square root y^2

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[skeeter]

to rationalize, multiply numerator and denominator by the conjugate of the denominator ...

\(\displaystyle \L \frac{\sqrt{x}+2}{3 - \sqrt{x}} \cdot \frac{3 + \sqrt{x}}{3 + \sqrt{x}} =\frac{x + 5\sqrt{x} + 6}{9 - x}\)

I'm guessing you mean the following on your 2nd problem ...

\(\displaystyle \L (3y^2)^{\frac{1}{3}} \cdot (y^2)^{\frac{1}{4}} =\)

\(\displaystyle \L 3^{\frac{1}{3}}y^{\frac{2}{3}} \cdot y^{\frac{1}{2}} =\)

\(\displaystyle \L 3^{\frac{1}{3}}y^{\frac{5}{6}} = 3^{\frac{2}{6}}y^{\frac{5}{6}} = (9y^5)^{\frac{1}{6}}\)

 

[pka]

There is a minor correction. We need to use absolute values.
\(\displaystyle \L (3y^2)^{\frac{1}{3}} \cdot (y^2)^{\frac{1}{4}} =\)

\(\displaystyle \L 3^{\frac{1}{3}}y^{\frac{2}{3}} \cdot \|y\|^{\frac{1}{2}} =\)

\(\displaystyle \L 3^{\frac{1}{3}}y^{\frac{5}{6}} = 3^{\frac{2}{6}}\|y\|^{\frac{5}{6}} = (9\|y\|^5)^{\frac{1}{6}}\)