Question

Which of thw following is equivalent to tosq root of -50

Answer 1

• i = $\sqrt{-1}$
• Product rule of radicals: √ab = √a x √b

Firstly, factor out i: $i\sqrt{50}$

Next, apply the product rule of radicals here as such:

$i\sqrt{50}=i\sqrt{10\times 5}=i\sqrt{5\times 2\times 5}=5i\sqrt{2}$

Your answer is 5i√2, or the second option.

Answer 2

just to add to @GoddessofDork superb reply above.

$\bf \sqrt{-50}\implies \sqrt{-1\cdot 50}\implies \sqrt{-1}\cdot \sqrt{50}~~ \begin{cases} 50=2\cdot 5\cdot 5\\ \qquad 2\cdot 5^2 \end{cases}\implies \sqrt{-1}\cdot \sqrt{2\cdot 5^2} \\\\\\ i\cdot 5\sqrt{2}\implies 5i\sqrt{2}$