Simplify Radical sqrt(65/7)/[2sqrt(2)] | Step-by-Step Guide & Explanation

[js14]

sqrt(65/7)/[2sqrt(2)] I know how to simplfy radicals but this one has me stuck. I tried to answer it and i got sqrt(65)/[2*sqrt(2)] is this right?

 

[Mark44]

sqrt(65/7)/[2sqrt(2)] I know how to simplfy radicals but this one has me stuck. I tried to answer it and i got sqrt(65)/[2*sqrt(2)] is this right?

No.

You lost sqrt(7) somehow.

This is the same as
$$\frac{\sqrt{65}}{\sqrt{7}} \cdot \frac{1}{2\sqrt{2}}$$

Multiply by 1 in the form of sqrt(14)/sqrt(14) to rationalize the denominator.

 

[js14]

Ok I get 1/2 * sqrt(65/14). is this right?

 

[ojs]

yes, that is correct.

you can also simplify this by doing the following

$$\frac{\sqrt{65}}{\sqrt{7}} \cdot \frac{1}{2\sqrt{2}} = \frac{1}{2} \frac{\sqrt{65}}{\sqrt{7} \sqrt{2}} = \frac{1}{2} \frac{\sqrt{65}}{\sqrt{7 \cdot 2}} = \frac{1}{2} \sqrt{\frac{65}{14}}$$

 

[Mark44]

Often the textbook's answer will appear without radicals in the denominator. If that's the case in your textbook, multiply the answer that ojs gave by sqrt(14)/sqrt(14), which gives
$$\frac{\sqrt{910}}{28}$$

 

[js14]

Thanks!