Question

Simplify and comment on the result of the expression: $\frac{\sqrt{5}}{\frac{17}{50}+\frac{4}{25}}$

• A. It is a non-terminating and non-repeating decimal number.
• B. It is a non-terminating and repeating decimal number.
• C. It is not an real number.

Answer 1

The correct option is A It is a non-terminating and non-repeating decimal number.

Let's simplify:

$\frac{\sqrt{5}}{\frac{17}{50}+\frac{4}{25}}$
$=\frac{\sqrt{5}}{\frac{17+4\times 2}{50}}$
$=\frac{\sqrt{5}}{\frac{25}{50}}$
$=\frac{\sqrt{5}}{\frac{1}{2}}$
$=2\times \sqrt{5}$
$=2\times \mathrm{2.236...}$
$=\mathrm{4.472...}$

It is a non-terminating and non-repeating decimal number, i.e., an irrational number.