Question

simplify: \frac{10 - \sqrt{75}}{5}

Explanation:

Simplify the radical term

$$ \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3} $$

Substitute and factor the numerator

$$ \frac{10 - \sqrt{75}}{5} = \frac{10 - 5\sqrt{3}}{5} = \frac{5(2 - \sqrt{3})}{5} $$

Divide out the common factor

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

Answer:

\(2 - \sqrt{3}\)