Question

simplify by rationalizing the denominator.
$-dfrac{7}{sqrt{11}}$

Explanation:

Step1: Multiply numerator and denominator by $\sqrt{11}$

To rationalize the denominator, we multiply the numerator and the denominator by the square root in the denominator, which is $\sqrt{11}$. So we have:
$$-\frac{7}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}}$$

Step2: Simplify the expression

When we multiply the numerators, we get $7\times\sqrt{11} = 7\sqrt{11}$, and when we multiply the denominators, we get $\sqrt{11}\times\sqrt{11}=11$ (since $\sqrt{a}\times\sqrt{a} = a$ for $a\geq0$). So the expression becomes:
$$-\frac{7\sqrt{11}}{11}$$

Answer:

$-\dfrac{7\sqrt{11}}{11}$