Question

Look at the rational expression shown below and rewrite it in simplified radical form. Please show ALL work!

Answer 1

Answer:

$\frac{1-\sqrt{7} }{2}$

Step-by-step explanation:

given $\frac{5-2\sqrt{7} }{3-\sqrt{7} }$

To rationalise the denominator multiply the numerator/ denominator by the conjugate of the denominator.

the conjugate of 3 - $\sqrt{7}$ is 3 + $\sqrt{7}$, hence

$\frac{5-2\sqrt{7} }{3-\sqrt{7} }$ × $\frac{3+\sqrt{7} }{3+\sqrt{7} }$

=  (15 + 5$\sqrt{7}$ - 6$\sqrt{7}$ - 14 ) / (9 - 7)

= $\frac{1-\sqrt{7} }{2}$ ← in simplified radical form