Question

Answer 1

`sqrt 2 K = sqrt(8 - 2 sqrt 7) - sqrt(8 + 2 sqrt 7)`

`= sqrt(7 - 2 sqrt 7 +1) - sqrt(7+ 2 sqrt 7 +1)`

`= sqrt 7 - 1 - sqrt 7 - 1`

`= -2 -> K=-sqrt 2`.

Answer 2

\(K=\dfrac{\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{7}-1-\left(\sqrt{7}+1\right)}{\sqrt{2}}=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)