Question

simplify.\\(sqrt{24} + sqrt{486}\\)\\(\boxed{?}sqrt{\boxed{}}\\)

Explanation:

Step1: Simplify $\sqrt{24}$

Factor 24 into $4\times6$, and since $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a\geq0,b\geq0$), we have $\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}$.

Step2: Simplify $\sqrt{486}$

Factor 486 into $81\times6$, then $\sqrt{486}=\sqrt{81\times6}=\sqrt{81}\times\sqrt{6}=9\sqrt{6}$.

Step3: Add the simplified radicals

Now, $\sqrt{24}+\sqrt{486}=2\sqrt{6}+9\sqrt{6}$. Since like radicals (radicals with the same radicand) can be added by adding their coefficients, we get $(2 + 9)\sqrt{6}=11\sqrt{6}$.

Answer:

$11\sqrt{6}$ (So the coefficient is 11 and the radicand is 6)