How do you rationalize the denominator of 5 over square root of 3?

Oct 12, 2015

Answer:

$\frac{5 \sqrt{3}}{3}$

Explanation:

To razionalize means to get rid of roots at the denominator. Since $\sqrt{a} \cdot \sqrt{a} = {\left(\sqrt{a}\right)}^{2} = a$, then we can multiply our fraction by $1$, so that we won't change its value, but we will write $1$ in a smart form, in this case $\frac{\sqrt{3}}{\sqrt{3}}$. Doing the multiplication, we get

$\frac{5}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{5 \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{5 \sqrt{3}}{3}$.