Is there any way I can simplify the equation $ \sqrt{a-b}-\sqrt{a}$ ?
I understand that there is no way to simplify $ \sqrt{a} - \sqrt{b} $
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3If you could simply $\sqrt{a}-\sqrt{a-b}$, you could simplify $\sqrt{a}-\sqrt{c}$ by setting $b=a-c$. – J.G. Nov 09 '21 at 13:20
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Generally, no. $\sqrt{a-b}-\sqrt{a}$ is as simplified as it will be. There do exist some special cases of course for specific values. – JMoravitz Nov 09 '21 at 13:50
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When $|b| < |a|$, it is sometimes helpful to write it $$\sqrt{a-b} - \sqrt{a}=\sqrt{a}\left(\sqrt{1-\tfrac{b}{a}} - 1\right).$$ You can then apply the binomial theorem. – WA Don Nov 10 '21 at 06:26