What is the value of the expression $\dfrac13\sqrt{\dfrac{12}{4}}-\left(\dfrac{9\cdot 5^{-2}}{0,5\cdot 2^{-1}}\right)^{-0,5}$?

Question

$$\dfrac13\sqrt{\dfrac{12}{4}}-\left(\dfrac{9\cdot 5^{-2}}{0,5\cdot 2^{-1}}\right)^{-0,5}$$

$$\frac{\sqrt{3}}{3} - \frac{\sqrt{25}}{\sqrt{36}}$$

Answer 1

Note that $$\dfrac{\sqrt{25}}{\sqrt{36}}=\frac{5}{6}.$$ Thus

$$\dfrac{\sqrt{3}}{3}-\dfrac{5}{6}=\dfrac{2\sqrt{3}-5}{6}.$$