How do you simplify sqrt39/sqrt26?

Apr 7, 2018

See a solution process below:

Explanation:

First, rewrite the numerator and denominator as:

$\frac{\sqrt{13 \cdot 3}}{\sqrt{13 \cdot 2}} \implies \frac{\sqrt{13} \sqrt{3}}{\sqrt{13} \sqrt{2}}$

We can next cancel the common terms in the numerator and denominator:

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{13}}}} \sqrt{3}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{13}}}} \sqrt{2}} \implies \frac{\sqrt{3}}{\sqrt{2}}$

Now, if necessary we can rationalize the denominator by multiplying the fraction by the appropriate form of $1$:

$\frac{\sqrt{2}}{\sqrt{2}} \times \frac{\sqrt{3}}{\sqrt{2}} \implies$

$\frac{\sqrt{2} \times \sqrt{3}}{\sqrt{2} \times \sqrt{2}} \implies$

$\frac{\sqrt{2 \times 3}}{2} \implies$

$\frac{\sqrt{6}}{2}$