Question

simplify:
2√24

Explanation:

Step1: Factor the radicand

Factor 24 into a product of a perfect square and another number: $24 = 4\times6$, where 4 is a perfect square. So, $\sqrt{24}=\sqrt{4\times6}$.

Step2: Use the square - root property

According to the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a\geq0,b\geq0$), we have $\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}$. Since $\sqrt{4} = 2$, then $\sqrt{24}=2\sqrt{6}$.

Step3: Multiply by the coefficient outside the radical

We have $2\sqrt{24}=2\times(2\sqrt{6})$. Multiply the coefficients: $2\times2 = 4$. So, $2\sqrt{24}=4\sqrt{6}$.

Answer:

$4\sqrt{6}$