Question

What is the answer to the question?

Answer 1

9514 1404 393

Answer:

  C)  √3

Step-by-step explanation:

The repeating decimals are both single digits, beginning at the decimal point. So, their equivalent is that digit divided by 9:

  $0.\overline{4}=\dfrac{4}{9}\\\\0.\overline{9}=\dfrac{9}{9}=1$

This means the given expression can be simplified to ...

  $\dfrac{3\sqrt{0.\overline{4}}+\sqrt{0.\overline{9}}}{\sqrt{3}}=\dfrac{3\sqrt{\dfrac{4}{9}}+\sqrt{\dfrac{9}{9}}}{\sqrt{3}}=\dfrac{3\cdot\dfrac{2}{3}+1}{\sqrt{3}}=\dfrac{3}{\sqrt{3}}=\boxed{\sqrt{3}}$