Answer:
The correct option is A) It is rational and equal to 12.
Step-by-step explanation:
Consider the provided information.
The provided expression is:
[tex]\sqrt{2} (3\sqrt{2}+\sqrt{18})[/tex]
Further simplify the above expression.
[tex]\sqrt{2} (3\sqrt{2}+\sqrt{2\times\ 3 \times3})[/tex]
[tex]\sqrt{2} (3\sqrt{2}+3\sqrt{2})[/tex]
Now, use the distributive property: [tex]a(b+c)=ab+ac[/tex]
[tex]3\sqrt{2}\times {\sqrt{2}} +3\sqrt{2}\times{\sqrt{2}}[/tex]
[tex]3\times{2}+3\times{2}[/tex]
[tex]6+6[/tex]
[tex]12[/tex]
As 12 is a rational number. Thus, the correct option is A) It is rational and equal to 12.
