Question

1/2underroot486-underroot27/2

Answer 1

$\frac{1}{2} \sqrt{486} - \sqrt{ \frac{27}{2} } \\ \\ = \frac{1}{2} \sqrt{2\times 3^5 } - \sqrt{ \frac{3^3}{2} } \\ \\ = \sqrt{ \frac{2\times 3^5}{4} }- \sqrt{ \frac{3^3}{2} } \\ \\ = \sqrt{ \frac{3^5}{2} }- \sqrt{ \frac{3^3}{2} } \\ \\= \sqrt{ \frac{3^4\times 3}{4} }- \sqrt{ \frac{3^2 \times 3}{2} } \\ \\= 9\sqrt{ \frac{3}{2} }- 3\sqrt{ \frac{3}{2} } \\ \\ =\boxed{6\sqrt{ \frac{3}{2} }}\ or\ \boxed{7.35}$