Question

simplify by rationalizing the denominator.
$-\frac{1}{9sqrt{13}}$
bol ($sqrt{square}$), type
oot\

Explanation:

Step1: Multiply numerator and denominator by $\sqrt{13}$ to rationalize the denominator.

To rationalize the denominator of a fraction with a square root in the denominator, we multiply the numerator and the denominator by that square root. So we have:
$$-\frac{1}{9\sqrt{13}} \times \frac{\sqrt{13}}{\sqrt{13}}$$

Step2: Simplify the numerator and the denominator.

The numerator becomes $1\times\sqrt{13}=\sqrt{13}$, and the denominator becomes $9\sqrt{13}\times\sqrt{13}=9\times13 = 117$ (since $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$). So the fraction simplifies to:
$$-\frac{\sqrt{13}}{117}$$

Answer:

$-\dfrac{\sqrt{13}}{117}$