a)
[tex]\it\sqrt{45}=\sqrt{9\cdot5}=3\sqrt5\\\\\sqrt{61\dfrac{1}{4}}=\sqrt{\dfrac{245}{4}}=\dfrac{\sqrt{5\cdot49}}{2}=\dfrac{7\sqrt5}{2}\\\\11\sqrt{1\dfrac{1}{4}}=11\sqrt{\dfrac{5}{4}}=11\cdot\dfrac{\sqrt5}{2}=\dfrac{11\sqrt5}{2}\\\\E = 3\sqrt5+\dfrac{7\sqrt5}{2}-\dfrac{11\sqrt5}{2}=3\sqrt5-\dfrac{4\sqrt5}{2}=3\sqrt5-2\sqrt5=\sqrt5[/tex]
b)
[tex]\it\sqrt{7+4\sqrt3}=\sqrt{4+3+4\sqrt3}=\sqrt{2^2+4\sqrt3+(\sqrt3)^2}=\sqrt{(2+\sqrt3)^2} =\\ \\=|2+\sqrt3|=2+\sqrt3\\\\Analog,\ \ \sqrt{7-4\sqrt3}=2-\sqrt3\\\\E = (2+\sqrt3+2-\sqrt3)^2=4^2=16[/tex]
