Question

$\frac{3}{2} \times \sqrt{90} - \frac{1}{4} \times \sqrt{250} + \frac{2}{5} \times \sqrt{50}$

Answer 1

$\ \ \ \frac{2}{3} \times \sqrt{90} - \frac{1}{4} \times \sqrt{250} + \frac{2}{5} \times \sqrt{50} \\ \\= \frac{2}{3} \times \sqrt{9\cdot10} - \frac{1}{4} \times \sqrt{25\cdot10} + \frac{2}{5} \times\sqrt{25\cdot2} \\ \\= \frac{2}{3} \times \sqrt{9}\cdot\sqrt{10} - \frac{1}{4} \times \sqrt{25}\cdot \sqrt{10} + \frac{2}{5} \times \sqrt{25}\cdot \sqrt{2} \\ \\= \frac{2}{3} \times3\cdot\sqrt{10} - \frac{1}{4} \times 5\cdot \sqrt{10} + \frac{2}{5} \times5\cdot \sqrt{2}$
$\\= \frac{6}{3}\cdot\sqrt{10} - \frac{5}{4}\cdot \sqrt{10} + \frac{10}{5}\cdot \sqrt{2} \\ \\=2\cdot\sqrt{10} - \frac{5}{4}\cdot \sqrt{10} +2\cdot \sqrt{2} \\ \\=2\sqrt{10} - \frac{5}{4} \sqrt{10} +2\sqrt{2} \\ \\=\frac{8\sqrt{10} }{4}- \frac{5\sqrt{10} }{4} +2\sqrt{2} \\ \\= \frac{3\sqrt{10} }{4} +2\sqrt{2}$