Simplify the expression. √12/√5

To simplify the expression ( frac{sqrt{12}}{sqrt{5}} ), you can first combine the square roots:

[

frac{sqrt{12}}{sqrt{5}} = sqrt{frac{12}{5}}

]

Next, simplify ( sqrt{12} ) as follows:

[

sqrt{12} = sqrt{4 times 3} = sqrt{4} cdot sqrt{3} = 2sqrt{3}

]

Now, substitute this back into the expression:

[

sqrt{frac{12}{5}} = frac{2sqrt{3}}{sqrt{5}}

]

To rationalize the denominator, multiply the numerator and the denominator by ( sqrt{5} ):

[

frac{2sqrt{3} cdot sqrt{5}}{sqrt{5} cdot sqrt{5}} = frac{2sqrt{15}}{5}

]

So, the simplified expression is:

[

boxed{frac{2sqrt{15}}{5}}

]

The correct answer is ( frac{2sqrt{15}}{5} ).