Question

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

Answer 1

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