Question

rationalize and simplify completely: √6 over √5

Answer 1

The only thing to this is...

$\mathrm{Combine\:same\:powers}\:: \frac{\sqrt{x}}{\sqrt{y}}=\sqrt{\frac{x}{y}} \ \textgreater \ \sqrt{\frac{6}{5}}$

Hope this helps!

Answer 2

For this to be simplified completely, there cannot be a square root in the denominator of the fraction. So to simplify this, you must multiply the top and bottom of the fraction by √5

$\frac{ \sqrt{6} }{ \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }$

When you multiply a square root by itself you get the number that is under the square root. This means hat when we multiply √5 by √5 it becomes 5.

For the top of the fraction when we multiply √6 by √5 we multiply the 6 and 5 together and keep it under the square root.

Thus making $\frac{ \sqrt{6} }{ \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }$ ...

$\frac{ \sqrt{30} }{5}$

Hope this helps!