Question

Answer 1

\(a,\dfrac{\sqrt{72}}{\sqrt{2}}=\dfrac{6\sqrt{2}}{\sqrt{2}}=6;\dfrac{\sqrt{192}}{\sqrt{12}}=\sqrt{\dfrac{192}{12}}=\sqrt{16}=4\\ b,=\dfrac{\sqrt{\left(\sqrt{a}-\sqrt{b}\right)^2}}{\sqrt{\sqrt{a}-\sqrt{b}}}=\sqrt{\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}}=\sqrt{\sqrt{a}-\sqrt{b}}\\ c,\dfrac{\sqrt{x-3}}{\sqrt{\sqrt{x}+\sqrt{3}}}:\dfrac{\sqrt{\sqrt{x}-\sqrt{3}}}{\sqrt{3}}\\ =\dfrac{\sqrt{\left(\sqrt{x}-\sqrt{3}\right)\left(\sqrt{x}+\sqrt{3}\right)}}{\sqrt{\sqrt{x}+\sqrt{3}}}\cdot\dfrac{\sqrt{3}}{\sqrt{\sqrt{x}-\sqrt{3}}}\\ =\sqrt{3}\)