Question

simplify.
\sqrt{24}+\sqrt{486}
?\sqrt{}

Explanation:

Step1: Simplify $\sqrt{24}$

We know that $24 = 4\times6$, so $\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}$.

Step2: Simplify $\sqrt{486}$

We find the prime - factorization of $486 = 2\times3^5$. Then $\sqrt{486}=\sqrt{2\times3^5}=\sqrt{2\times3^4\times3}=\sqrt{3^4}\times\sqrt{2\times3}=9\sqrt{6}$.

Step3: Combine the two simplified terms

$\sqrt{24}+\sqrt{486}=2\sqrt{6}+9\sqrt{6}=(2 + 9)\sqrt{6}=11\sqrt{6}$.

Answer:

$11\sqrt{6}$