Question

After rationalising the denominator of $\frac{7}{3\sqrt{3}-2\sqrt{2}}$, we get the denominator of the resultant equivalent expression as:

• A. $5$
• B. $13$
• C. $19$
• D. $35$

Answer 1

The correct option is C $19$

$\frac{7}{3\sqrt{3}-2\sqrt{2}}=\frac{7}{3\sqrt{3}-2\sqrt{2}}\times \left(\frac{3\sqrt{3}+2\sqrt{2}}{3\sqrt{3}+2\sqrt{2}}\right)=\frac{7(3\sqrt{3}+2\sqrt{2})}{27-8}=\frac{7(3\sqrt{3}+2\sqrt{2})}{19}$. Hence, the denominator of the equivalent expression is $19.$