Simplify $ \frac{1}{3-\sqrt{2}} $ in the form of p + q√2

Assessment: JAMB UTME - Mathematics - 2022 Subject: General Mathematics

Question 1 Report

\frac{7}{3}

\frac{1}{7 \sqrt 2}

\frac{7}{3}

\frac{1}{7 \sqrt 2}

\frac{3}{7}

\frac{1}{7 \sqrt 2}

\frac{3}{7}

\frac{\sqrt 2}{7}

Answer Details

Rationalization with conjugate $3 + \sqrt 2$

$\frac{1}{3 - \sqrt 2}$

→ $\frac{1 * [3 + \sqrt 2]}{[3 - \sqrt 2] [3 + \sqrt 2]}$

= $\frac{3 + \sqrt 2}{9 - 3 \sqrt 2 + 3 \sqrt 2 + \sqrt 4}$

= $\frac{3 + \sqrt 2}{9 - 2}$ → $\frac{3 + \sqrt 2}{7}$

= $\frac{3}{7}$ + $\frac{\sqrt 2}{7}$ $\frac{3}{7}$

Simplify \( \frac{1}{3-\sqrt{2}} \) in the form of p + q√2