Question

Write an equivalent expression by rationalizing the denominator $\frac{1}{6-\sqrt{10}}$

• A. $\frac{6-\sqrt{10}}{26}$
  
• B. $\frac{6+\sqrt{10}}{26}$
  
• C. $\frac{26}{6+\sqrt{10}}$
  
• D. $\frac{26}{6-\sqrt{10}}$
  

Answer 1

The correct option is B $\frac{6+\sqrt{10}}{26}$


To rationalize the denominator of $\frac{1}{6-\sqrt{10}}$, multiply the denominator with its conjugate pair.
The conjugate pair of $6-\sqrt{10}$ is $6+\sqrt{10}$.

Let's multiply both the numerator and denominator with $6+\sqrt{10}$.

$\frac{1}{6-\sqrt{10}}=\frac{1}{6-\sqrt{10}}\times 1$
$=\frac{1}{6-\sqrt{10}}\times \frac{6+\sqrt{10}}{6+\sqrt{10}}$

$=\frac{6+\sqrt{10}}{6^2-(\sqrt{10}{)}^2}$

$=\frac{6+\sqrt{10}}{36-10}$

$=\frac{6+\sqrt{10}}{26}$