a) \(\sqrt{33-12\sqrt{6}}+\sqrt{15+6\sqrt{6}}=\sqrt{24-2.2\sqrt{6}.3+9}+\sqrt{6+2.\sqrt{6}.3+9}=\sqrt{\left(2\sqrt{6}-3\right)^2}+\sqrt{\left(\sqrt{6}+3\right)^2}=\left|2\sqrt{6}-3\right|+\left|\sqrt{6}+3\right|=2\sqrt{6}-3+\sqrt{6}+3=3\sqrt{6}\)
b) \(\dfrac{\sqrt{99}}{\sqrt{11}}+\dfrac{\sqrt{28}}{\sqrt{7}}-\sqrt{\sqrt{81}}=\sqrt{\dfrac{99}{11}}+\sqrt{\dfrac{28}{7}}-\sqrt{9}=\sqrt{9}+\sqrt{4}-\sqrt{9}=\sqrt{4}=2\)
a) \(\sqrt{33-12\sqrt{6}}\) + \(\sqrt{15+6\sqrt{6}}\)
= \(\sqrt{9-2.3.2\sqrt{6}+24}\)+\(\sqrt{9+2.3\sqrt{6}+6}\)
= \(\sqrt{\left(3-2\sqrt{6}\right)^2}\)+\(\sqrt{\left(3+\sqrt{6}\right)^2}\)
=\(\left|3-2\sqrt{6}\right|+\left|3+\sqrt{6}\right|\)
=\(2\sqrt{6}-3+3+\sqrt{6}\)
=\(\sqrt{6}\)
b)\(\dfrac{\sqrt{99}}{\sqrt{11}}\)+\(\dfrac{\sqrt{28}}{\sqrt{7}}\)\(-\sqrt{\sqrt{81}}\)
= \(\sqrt{\dfrac{99}{11}}+\sqrt{\dfrac{28}{7}}-3\)
=\(\sqrt{9}+\sqrt{4}-3\)
= 3+2-3
= 2
a) \(\sqrt{33-12\sqrt{6}}+\sqrt{15+6\sqrt{6}}\)
=\(\sqrt{24-2.2\sqrt{6}.3+9}\)+\(\sqrt{9+2.3\sqrt{6}+6}\)
=\(\sqrt{\left(2\sqrt{6}-3\right)^2}+\sqrt{\left(3+\sqrt{6}\right)^2}\)
=\(\left|2\sqrt{6}-3\right|+\left|3+\sqrt{6}\right|\)
=\(2\sqrt{6}-3+3+\sqrt{6}=3\sqrt{6}\)
