Question

Express the sum of (square root) -64 and 3(square root) -4 as a monomial in terms of I.

Answer 1

$\bf \sqrt{-64}~+~3\sqrt{-4}\implies \sqrt{-1\cdot 2^6}~+~3\sqrt{-1\cdot 2^2} \\\\\\ \sqrt{-1}\cdot \sqrt{2^6}~+~3\sqrt{-1}\cdot \sqrt{2^2}\implies i\cdot \sqrt{2^{3\cdot 2}}~+~3\cdot i\cdot 2 \\\\\\ i\cdot \sqrt{(2^3)^2}~~+~~6i\implies 2^3i~+~6i\implies 8i+6i\implies 14i$