Question

For $\frac{3\sqrt{4}-\sqrt{6}}{3\sqrt{3}+4\sqrt{4}}$, choose the appropriate expression from the options below:

• A. Rationalising factor is $3\sqrt{3}+4\sqrt{4}$
• B. Rationalising factor is $3\sqrt{3}-4\sqrt{4}$
• C. Rationalising factor is $3\sqrt{4}-\sqrt{6}$
• D. Rationalising factor is $3\sqrt{4}+\sqrt{6}$

Answer 1

The correct option is B Rationalising factor is $3\sqrt{3}-4\sqrt{4}$

Given,
$\frac{3\sqrt{4}-\sqrt{6}}{3\sqrt{3}+4\sqrt{4}}$
The denominator is $3\sqrt{3}+4\sqrt{4}$
The conjugate of the denominator is $3\sqrt{3}-4\sqrt{4}$

The rationalizing factor is the conjugate of the denominator

$\therefore$ The rationalizing factor is $3\sqrt{3}-4\sqrt{4}$