$2\sqrt{x} + \sqrt{3}$

How do I simplify this?

  • 9
    $\begingroup$ It can’t be simplified any further. $\endgroup$ Oct 3 '11 at 23:25
  • $\begingroup$ Check the edit. I left something out. $\endgroup$
    – David
    Oct 3 '11 at 23:28
  • 2
    $\begingroup$ That doesn't make it any better. $\endgroup$
    – joriki
    Oct 3 '11 at 23:32
  • 2
    $\begingroup$ Brian's comment still applies, even after your edit. $\endgroup$ Oct 3 '11 at 23:32
  • 4
    $\begingroup$ What's not simple about that? $\endgroup$
    – davidlowryduda
    Oct 4 '11 at 0:47

This seems a simpler derivation to me:

Squaring $a \sqrt x + \sqrt b$ we get $a^2 x + b + 2a \sqrt{bx}$ so $$ a \sqrt x + \sqrt b = \sqrt{a^2 x + b + 2a \sqrt{bx}}. $$

This seems to be a more complicated result to me.

I know, it's all about me.


Maybe you are searching for something similar to this:

$$\sqrt{a{^+ _-}\sqrt{b}}=\sqrt{\frac{a+c}{2}}{^+ _-}\sqrt{\frac{a-c}{2}}$$


A example:


In your problem:








The final is:


But it needs a better investigation of the existence conditions in these calculus.

  • 5
    $\begingroup$ I haven't followed the details of the calculations, but how is the final result supposed to be simpler than $2\sqrt{x} + \sqrt{3}$? $\endgroup$
    – t.b.
    Nov 11 '11 at 1:36
  • 1
    $\begingroup$ It's no simpler (I wrote Maybe you are searching for something similar to this:), it's just a transformation and maybe was he is looking for. If he tells not I'll delete if none think this useful. $\endgroup$
    – GarouDan
    Nov 16 '11 at 13:26
  • $\begingroup$ Compare with my Simple Denesting Formula. $\endgroup$ Dec 11 '11 at 17:49

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