Question

Answer 1

\(\dfrac{5\sqrt{60}.3\sqrt{15}}{15\sqrt{50}.2\sqrt{18}}=\dfrac{10\sqrt{15}.3.\sqrt{15}}{75\sqrt{2}.6\sqrt{2}}=\dfrac{450}{900}=\dfrac{1}{2}\)

\(\sqrt{27\left(\sqrt{3}-\sqrt{5}\right)^2}=\sqrt{27}.\left(\sqrt{5}-\sqrt{3}\right)=3\sqrt{15}-9\)

\(\dfrac{x-2}{\sqrt{x^2-4x+4}}=\dfrac{x-2}{\left|x-2\right|}=\left[{}\begin{matrix}-1\\1\end{matrix}\right.\)

Answer 2

d) \(\dfrac{x-2}{\sqrt{x^2-4x+4}}=\dfrac{x-2}{\left|x-2\right|}=\pm1\)

b) \(\sqrt{27\cdot\left(\sqrt{3}-\sqrt{5}\right)^2}=3\sqrt{3}\cdot\left(\sqrt{5}-\sqrt{3}\right)=3\sqrt{15}-9\)