Question

√-60
2i√5
2i√22
6i√2
2i√15

Explanation:

Step1: Rewrite -60 as -1×60

$\sqrt{-60}=\sqrt{-1\times60}$

Step2: Use the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = - 1$, $b = 60$)

$\sqrt{-1\times60}=\sqrt{-1}\cdot\sqrt{60}$

Step3: Recall that $\sqrt{-1}=i$ and factorize 60

Since $\sqrt{-1}=i$ and $60 = 4\times15$, then $\sqrt{60}=\sqrt{4\times15}=\sqrt{4}\cdot\sqrt{15}=2\sqrt{15}$

Step4: Combine the results

$\sqrt{-1}\cdot\sqrt{60}=i\times2\sqrt{15}=2i\sqrt{15}$

Answer:

$2i\sqrt{15}$