Question

What is the answer to the question?

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Answer 1

9514 1404 393

Answer:

C) √3

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}=(4)/(9)\\\\0.\overline{9}=(9)/(9)=1`

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

`\frac{3\sqrt{0.\overline{4}}+\sqrt{0.\overline{9}}}{√(3)}=\frac{3\sqrt{(4)/(9)}+\sqrt{(9)/(9)}}{√(3)}=(3\cdot(2)/(3)+1)/(√(3))=(3)/(√(3))=\boxed{√(3)}`