Question

Given that $\sqrt{3}=1.7321$, find the value of $100$ times the given expression $\sqrt{192}-\frac{1}{2}\sqrt{48}-\sqrt{75}$.

Answer 1

Consider$100(\sqrt{192}-\frac{1}{2}\sqrt{48}-\sqrt{75})$ and solve as follows:

$100(\sqrt{192}-\frac{1}{2}\sqrt{48}-\sqrt{75})$

$=100(\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 3}-\frac{1}{2}\sqrt{2\times 2\times 2\times 2\times 3}-\sqrt{5\times 5\times 3})$

$=100(\sqrt{{\left(8\right)}^2\times 3}-\frac{1}{2}\sqrt{{\left(4\right)}^2\times 3}-\sqrt{{\left(5\right)}^2\times 3})=100(8\sqrt{3}-\frac{4}{2}\sqrt{3}-5\sqrt{3})$

$=100(8\sqrt{3}-2\sqrt{3}-5\sqrt{3})=100\left(\sqrt{3}\right)$

$=100\times 1.7321=173.21$ .

Hence, $100(\sqrt{192}-\frac{1}{2}\sqrt{48}-\sqrt{75})=173.21$.