Answer:
[tex]\dfrac{2\sqrt{7}}{7}[/tex]
Step-by-step explanation:
There's a radical in the denominator of the fraction
[tex]\dfrac{2}{\sqrt{7}}[/tex].
Multiplying the denominator [tex]\sqrt{7}[/tex] by a certain number will get rid of its radical part. What number will serve the purpose? There's only one square root in the denominator, so multiplying the square root [tex]\sqrt{7}[/tex] by itself will do.
Multiple both the fraction by
[tex]\dfrac{\sqrt{7}}{\sqrt{7}}[/tex],
which is the same as multiplying by [tex]1[/tex],
will rationalize the denominator without changing the value of the fraction. Here's how it works:
[tex]\begin{array}{ll} \dfrac{2}{\sqrt{7}}\\= \dfrac{2}{\sqrt{7}} \times 1 & \text{Doing so does not change the value.}\\= \dfrac{2}{\sqrt{7}} \times \dfrac{\sqrt{7}}{\sqrt{7}} & \text{The value of} \; \dfrac{\sqrt{7}} {\sqrt{7}} \; \text{is} \; 1 \text{.} \\=\dfrac{2\sqrt{7}}{(\sqrt{7})^{2}} & \text{Square the square root} \; \sqrt{7}\text{.}\\= \dfrac{2\sqrt{7}}{7}\\\end{array}[/tex].
