Question

16)√15-√12 phần 2-√3 +12 phần 3+√3 + 9 phần √3

Answer 1

\(\frac{\sqrt{15}-\sqrt{12}}{2-\sqrt3}+\frac{12}{3+\sqrt3}+\frac{9}{\sqrt3}\)

\(=\frac{\left(\sqrt{15}-2\sqrt3\right)\left(2+\sqrt3\right)}{\left(2-\sqrt3\right)\left(2+\sqrt3\right)}+\frac{12\left(3-\sqrt3\right)}{\left(3+\sqrt3\right)\left(3-\sqrt3\right)}+3\sqrt3\)

\(=\left(\sqrt{15}-2\sqrt3\right)\left(2+\sqrt3\right)+\frac{12\cdot\left(3-\sqrt3\right)}{9-3}+3\sqrt3\)

\(=\left(\sqrt{15}-2\sqrt3\right)\left(2+\sqrt3\right)+2\left(3-\sqrt3\right)+3\sqrt3\)

\(=2\sqrt{15}+3\sqrt5-4\sqrt3-6+6-2\sqrt3+3\sqrt3=2\sqrt{15}+3\sqrt5-3\sqrt3\)