Question

Simplify please.

square root of 7 minus 1 over 2 square root of 7 plus 4 square root of 2

Answer 1

Short of solving it, I see this:\[\frac{\sqrt7 - 1}{2\sqrt7+4\sqrt2} \rightarrow \frac{\sqrt7 - 1}{2(\sqrt7+2\sqrt2)} \rightarrow \frac{1}{2}\times (\sqrt7 - 1)(\sqrt7+2\sqrt2)\]

Answer 2

\[\frac{1}{2} \times ( 7 + 2 \sqrt14 -\sqrt7 - 2\sqrt2)\]

Answer 3

\[\frac{7}{2} + \sqrt14 - \frac{\sqrt7}{2} - \sqrt2\]

Answer 4

Do you mean \[\sqrt{7}-{1 \over 2\sqrt{7}}+4\sqrt{2}?\]Or perhaps\[{\sqrt{7}-1 \over 2\sqrt{7}}+4\sqrt{2}?\]Could you please tell us exactly how the equation looks?

Answer 5

Wait

Answer 6

\[\sqrt{7}- 1 \over 2 \sqrt{7}+4\sqrt{2}\]

Answer 7

\[{\sqrt{7}- 1 \over 2 \sqrt{7}+4\sqrt{2}} =-{7\over2}-\sqrt2+{\sqrt7 \over 2}+\sqrt{14}\]eSpex just missed a sign change.

Answer 8

Oh. I don't really know how to answer the equation.

Answer 9

You want to know how to simplify it? This would be a good method.\[{\sqrt{7}- 1 \over 2 \sqrt{7}+4\sqrt{2}} \cdot {2\sqrt{7}-4\sqrt{2} \over 2\sqrt{7}-4\sqrt{2}}\]\[= {{14 -4\sqrt{14}-2\sqrt7 +4\sqrt{2}} \over (2\sqrt7)^2-(4\sqrt2)^2}\]\[= {{14 -4\sqrt{14}-2\sqrt7 +4\sqrt{2}} \over 28-32}\]\[={{14 -4\sqrt{14}-2\sqrt7 +4\sqrt{2}} \over -4}\]\[=-{7 \over 2}+\sqrt{14}+{\sqrt7 \over 2}-\sqrt2\]

Answer 10

Thanks a lot @eSpeX and @KingGeorge.

Answer 11

You're welcome.