4. Evaluate the following.
(iv)3√2(6√8+15√18-3√50)

(v)28√32 + 5√50 + 16√18 - 29√8

(vi)√3(3√48 + 9√27) - 2√3(2√75 - √300)

Dear Student,

Please find below the solution to the asked query:
$$\begin{gathered} \left(\mathrm{iv}\right)3\sqrt{2}\left(6\sqrt{8}+15\sqrt{18}-3\sqrt{50}\right) \\ \mathrm{Use} \sqrt{\mathrm{m}}\times \sqrt{\mathrm{n}}=\sqrt{\mathrm{mn}} \\ \Rightarrow \left(6\times 3\times \sqrt{2}\times \sqrt{8}\right)+\left(15\times 3\times \sqrt{2}\times \sqrt{18}\right)-\left(3\times 3\times \sqrt{2}\times \sqrt{50}\right) \\ \Rightarrow 18\sqrt{2\times 8}+45\sqrt{2\times 18}-9\sqrt{2\times 50} \\ \Rightarrow 18\sqrt{16}+45\sqrt{36}-9\sqrt{100} \\ \Rightarrow 18\times 4+45\times 6-9\times 10 \\ \Rightarrow 72+270-90 \\ \Rightarrow 252 \mathrm{Answer} \end{gathered}$$
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