Question

simplify. \\(sqrt{18} + 2sqrt{32}\\)

Explanation:

Step1: Simplify $\sqrt{18}$

Factor 18 into $9\times2$, so $\sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}$

Step2: Simplify $2\sqrt{32}$

Factor 32 into $16\times2$, so $2\sqrt{32}=2\times\sqrt{16\times2}=2\times\sqrt{16}\times\sqrt{2}=2\times4\sqrt{2}=8\sqrt{2}$

Step3: Add the simplified radicals

Now we have $3\sqrt{2}+8\sqrt{2}=(3 + 8)\sqrt{2}=11\sqrt{2}$

Answer:

$11\sqrt{2}$