Question

Help me

Answer 1

c)\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

=\(\dfrac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}-\dfrac{\sqrt{8+2\sqrt{7}}}{\sqrt{2}}\)

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

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

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

=\(\dfrac{-2}{\sqrt{2}}\)

=\(-\sqrt{2}\)