Question

simplify \\(\sqrt{6}\left(\sqrt{18} + \sqrt{8}\
ight)\\). the simplified expression is \\(\square\\).

Explanation:

Step1: Simplify square roots

Simplify $\sqrt{18}$ and $\sqrt{8}$. We know that $\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$ and $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$.

Step2: Distribute $\sqrt{6}$

Using the distributive property $a(b + c)=ab+ac$, we have $\sqrt{6}(\sqrt{18}+\sqrt{8})=\sqrt{6}\times\sqrt{18}+\sqrt{6}\times\sqrt{8}$.

Step3: Multiply square roots

Using the property $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$, we get:
$\sqrt{6}\times\sqrt{18}=\sqrt{6\times18}=\sqrt{108}=\sqrt{36\times3}=6\sqrt{3}$
$\sqrt{6}\times\sqrt{8}=\sqrt{6\times8}=\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}$

Step4: Combine like terms

Add the two terms: $6\sqrt{3}+4\sqrt{3}=(6 + 4)\sqrt{3}=10\sqrt{3}$

Answer:

$10\sqrt{3}$