Simplify the expression.
√12/√5
o 2√15
o 2√15/5
o 3√2
o I do not know the answer yet.
o √5
Simplify the expression. √12/√5
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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} ).