# Factoring out square roots from the numerator after rationalizing the denominator.

The question I was working on was to rationalize the denominator of $$\frac{1}{\sqrt{3}(\sqrt{21}+\sqrt{7})}$$

My answer was $$\frac{\sqrt7}{42}(3-\sqrt{3})$$.

But both my book and Symbolab gave the answer as $$\frac{1}{42}(3\sqrt{7}-\sqrt{21})$$.

Why shouldn't I factor out the $$\sqrt{7}$$?

$$\frac{\sqrt{7}}{42}\cdot(3-\sqrt{3}) = \frac{1}{42}\cdot\sqrt 7\cdot(3-\sqrt 3) = \frac{1}{42}\cdot(3\sqrt 7-\sqrt{21})$$
As another note, I think you started off by factoring $$\sqrt 7$$ in the denominator while the solutions given probably involved rationalizing immediately. It makes no difference anyway and both are acceptable.