Question

Rationalize denominator

Answer 1

Answer:

$\huge\boxed{\bf\:2}$

Step-by-step explanation:

$\frac{4}{3 + \sqrt{7}}$

Rationalise the denominator by multiplying the numerator & denominator of the fraction with $(3 - \sqrt{7})$.

$\frac{4\left(3-\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}$

Now, we  an see that the denominator is in the form of the algebraic identity: (x + y) (x - y) = x² - y². So,

$\frac{4\left(3-\sqrt{7}\right)}{3^{2}-\left(\sqrt{7}\right)^{2}} \\= \frac{4\left(3-\sqrt{7}\right)}{9-7} \\= \frac{4\left(3-\sqrt{7}\right)}{2}$

The new denominator is 2.

$\rule{150pt}{2pt}$

Answer 2

Answer:

Option D. 2

Step-by-step explanation:

Hello!

To rationalize the denominator, we should multiply the numerator and the denominator by the conjugate of the denominator. The conjugate simply means the same terms but with the opposite operation.

Rationalize

• $\frac4{3+\sqrt7}$
• $\frac4{3+\sqrt7} * \frac{3 - \sqrt7}{3 - \sqrt7}$
• $\frac{12 - 4\sqrt7}{9 - 7}$
• $\frac{12 - 4\sqrt7}{2}$

The new denominator is 2.