Question

Find the value of
${[4+3\sqrt{-20}]}^{1/2}+{[4-3\sqrt{-20}]}^{1/2}$

• A. $6$
• B. $2(3+\sqrt{5})$
• C. $2(3-\sqrt{5})$
• D. $2\sqrt{5}$

Answer 1

The correct option is A $6$

For alternate easier method of
$4+3\sqrt{-20}=4+i6\sqrt{5}$
Half the coefficient of i is $3\sqrt{5}$ and its factors are $3,\sqrt{5}$ such that $3^2-{\left(\sqrt{5}\right)}^2=4$
$\therefore E=(3+\sqrt{5})+(3-\sqrt{5})=6$
Ans: A