Answer:
Option B is correct.
The simplified form of the given expression is, [tex]18\sqrt{2}[/tex].
Explanation:
Given the expression: [tex]2\sqrt{18} +3 \sqrt{2} +\sqrt{162}[/tex]
Square root of a number is a value that when multiplied by itself, gives the number.
[tex]\sqrt{a^2}=\sqrt{a \times a}[/tex]= a
we can write the given expression as;
[tex]2\sqrt{9 \times 2} +3\sqrt{2} +\sqrt{2 \times 81}[/tex] or
[tex]2\sqrt{3^2 \times 2}+3 \sqrt{2} +\sqrt{9^2 \times 2}[/tex]
Then by definition of square root,
[tex]2 \cdot 3 \sqrt{2} +3\sqrt{2}+9 \sqrt{2}[/tex] or
[tex]6\sqrt{2} +3\sqrt{2} +9\sqrt{2} = 18\sqrt{2}[/tex]
Therefore, the simplified form of the given expression is, [tex]18\sqrt{2}[/tex] .
