Question

Answer 1

a: \(\sqrt{48}+2\sqrt{75}-6\sqrt{12}+\sqrt{27}\)

\(=4\sqrt3+2\cdot5\sqrt3-6\cdot2\sqrt3+3\sqrt3\)

\(=4\sqrt3+10\sqrt3-12\sqrt3+3\sqrt3=5\sqrt3\)

b: \(\sqrt{\left(\sqrt7-3\right)^2}-\sqrt7\)

\(=3-\sqrt7-\sqrt7=3-2\sqrt7\)

c: \(\frac{2}{\sqrt{11}-3}-\frac{2}{\sqrt{11}+3}\)

\(=\frac{2\left(\sqrt{11}+3\right)-2\left(\sqrt{11}-3\right)}{\left(\sqrt{11}-3\right)\left(\sqrt{11}+3\right)}\)

\(=\frac{2\sqrt{11}+6-2\sqrt{11}+6}{11-9}=\frac{12}{2}=6\)