Question

Simplify by rationalizing the denominator $\frac{5+3\sqrt{2}}{5-3\sqrt{2}}$

• A. $\frac{43+30\sqrt{5}}{7}$
• B. $\frac{41+30\sqrt{2}}{7}$
• C. $\frac{43+30\sqrt{2}}{5}$
• D. $\frac{43+30\sqrt{2}}{7}$

Answer 1

Answer: (D)

$\frac{43+30\sqrt{2}}{7}$

$\frac{5+3\sqrt{2}}{5-3\sqrt{2}}$
The conjugate of $5-3\sqrt{2}$ is $5+3\sqrt{2}$
$=\frac{5+3\sqrt{2}}{5-3\sqrt{2}}\times \frac{5+3\sqrt{2}}{5+3\sqrt{2}}$
$=\frac{(5+3\sqrt{2}{)}^2}{25-18}$
$=\frac{25+18+2\times 5\times 3\sqrt{2}}{7}$
$=\frac{43+30\sqrt{2}}{7}$