Question

which expression is equivalent to the given expression? \\(\frac{9}{sqrt{10}}\\) \
\\(\bigcirc\\) a. \\(3\sqrt{10}\\) \
\\(\bigcirc\\) b. \\(\frac{3}{sqrt{10}}\\) \
\\(\bigcirc\\) c. \\(\frac{9\sqrt{10}}{10}\\) \
\\(\bigcirc\\) d. \\(9\\) \
reset selection

Explanation:

Step1: Rationalize the denominator

To rationalize the denominator of $\frac{9}{\sqrt{10}}$, we multiply the numerator and the denominator by $\sqrt{10}$.
$$\frac{9}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}}$$

Step2: Multiply the numerators and denominators

Multiply the numerators: $9\times\sqrt{10} = 9\sqrt{10}$
Multiply the denominators: $\sqrt{10}\times\sqrt{10}=10$
So the expression becomes $\frac{9\sqrt{10}}{10}$

Answer:

C. $\frac{9\sqrt{10}}{10}$