[tex]a)\\\\\sqrt{\sqrt{256}} = \sqrt{\sqrt{16^{2}}} =\sqrt{16}=4\\\\lub\\\\((256)^\frac{1}{2}})^{\frac{1}{2}} = (4^{4})^{\frac{1}{2}\cdot\frac{1}{2}} = 4^{4\cdot\frac{1}{4}} = 4^{1} = 4[/tex]
[tex]b) \ \sqrt{\sqrt{\sqrt{\frac{4}{\sqrt{16}}}}} = \sqrt\sqrt\sqrt{\frac{4}{4}}}} = \sqrt\sqrt\sqrt{1} }}= \sqrt\sqrt{1} }=\sqrt{1} = 1[/tex]
[tex]c) \ \sqrt{2\sqrt{2\sqrt{2\cdot2}} }=\sqrt{2\sqrt{2\cdot2}} = \sqrt{2\cdot2} = \sqrt{2}[/tex]
