Question

Find the value of $\frac{1}{2}\sqrt{486}-\sqrt{\frac{27}{2}}$

Answer 1

Simplify the given expression:

$\begin{array}{l}\frac{1}{2}\sqrt{486}-\sqrt{\frac{27}{2}}\\ =\frac{1}{2}\sqrt{486}-\sqrt{\frac{27}{2}}\times \sqrt{\frac{2}{2}}\left(\text{Rationalising the expression}\right)\\ =\frac{1}{2}\sqrt{486}-\frac{\sqrt{27\times 2}}{2}\\ =\frac{1}{2}\sqrt{81\times 6}-\frac{\sqrt{3^2\times 3\times 2}}{2}\\ =\frac{1}{2}\sqrt{9^2\times 6}-\frac{3\sqrt{6}}{2}\\ =\frac{9}{2}\sqrt{6}-\frac{3\sqrt{6}}{2}\\ =\frac{6\sqrt{6}}{2}\\ =3\sqrt{6}\end{array}$

Hence, the value of $\frac{1}{2}\sqrt{486}-\sqrt{\frac{27}{2}}=3\sqrt{6}$