Question

After rationalizing the denominator of $\frac{7}{3\sqrt{3}-2\sqrt{2}}$, we get the denominator as:

• A. 13
• B. 19
• C. 5
• D. 35

Answer 1

The correct option is B

19

Explanation for the correct option:

Option (b): 19

The given expression is $\frac{7}{3\sqrt{3}-2\sqrt{2}}$.

We need to find the value of denominator.

Simplify it by multiplying the numerator and the denominator by the conjugate $\left(3\sqrt{3}+2\sqrt{2}\right)$of the denominator.

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

Simplify further, by using this identity $(a^2-b^2)=\left(a+b\right)\left(a-b\right)$

$=\frac{7(3\sqrt{3}+2\sqrt{2})}{{\left(3\sqrt{3}\right)}^2-{\left(2\sqrt{2}\right)}^2}$

$$\begin{gathered} =\frac{7(3\sqrt{3}+2\sqrt{2})}{9\left(3\right)-4\left(2\right)} \\ =\frac{21\sqrt{3}+14\sqrt{2}}{27-8} \\ =\frac{21\sqrt{3}+14\sqrt{2}}{19} \end{gathered}$$

Hence, the correct option is (b). The denominator is 19.