Question

8.5 divide radical expressions (homework)
score: 13/14 answered: 13/14
question 9
rationalize the denominator:
\\(\frac{\sqrt{3}}{7 - \sqrt{7}}=\\)
question help: video written example

Explanation:

Step1: Multiply by conjugate

Multiply the fraction $\frac{\sqrt{3}}{7 - \sqrt{7}}$ by $\frac{7+\sqrt{7}}{7+\sqrt{7}}$. We get $\frac{\sqrt{3}(7 + \sqrt{7})}{(7-\sqrt{7})(7+\sqrt{7})}$.

Step2: Expand the denominator

Use the difference - of - squares formula $(a - b)(a + b)=a^{2}-b^{2}$. Here $a = 7$ and $b=\sqrt{7}$, so $(7-\sqrt{7})(7+\sqrt{7})=7^{2}-(\sqrt{7})^{2}=49 - 7=42$.

Step3: Expand the numerator

Expand $\sqrt{3}(7+\sqrt{7})$ to get $7\sqrt{3}+\sqrt{21}$.

Answer:

$\frac{7\sqrt{3}+\sqrt{21}}{42}$