Question

What is the value obtained when we expand $({1+\sqrt{3})}^2$?

• A. $4+2\sqrt{3}$
• B. $2\sqrt{3}$
• C. 4
• D. $3+2\sqrt{3}$

Answer 1

The correct option is A $4+2\sqrt{3}$

Using the identity, $(a+b{)}^2=a^2+b^2+2ab$
${(1+\sqrt{3})}^2=1^2+(\sqrt{3}{)}^2+2\sqrt{3}=1+3+2\sqrt{3}=4+2\sqrt{3}$