Question

Which of the following expressions can be written as an integer?
I. ${(\sqrt{82}+\sqrt{82})}^2$
II. $\left(82\right)\left(\sqrt{82}\right)$
III. $\frac{(\sqrt{82}+\sqrt{82})}{82}$

• A. None
• B. I only
• C. III only
• D. I and II
• E. I and III

Answer 1

Answer: (B)

I only

I. ${(\sqrt{82}+\sqrt{82})}^2$ = $(2\sqrt{82}{)}^2$ = $4\times (\sqrt{82}{)}^2$ = $4\times 82=328\Rightarrow$ An Integer.

II. $\left(82\right)\left(\sqrt{82}\right)\Rightarrow$ Is in simplified form. Not an integer

III. $\frac{(\sqrt{82}+\sqrt{82})}{82}$

$\Rightarrow \frac{2\sqrt{82}}{82}$ $=\frac{\sqrt{82}}{41}\Rightarrow$ Not an interger.

So, option $B$ (I only) is the correct answer.