use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals…
use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals. -\\sqrt{-68}
Answer
Explanation:
Step1: Rewrite the negative - radicand
Recall that $\sqrt{-a}=i\sqrt{a}$ for $a>0$. So, $-\sqrt{-68}=-i\sqrt{68}$.
Step2: Simplify the radical
Factor 68: $68 = 4\times17$. Then $\sqrt{68}=\sqrt{4\times17}=\sqrt{4}\times\sqrt{17}=2\sqrt{17}$.
Step3: Combine the results
Substitute $\sqrt{68}=2\sqrt{17}$ into $-i\sqrt{68}$, we get $-2i\sqrt{17}$.
Answer:
$-2i\sqrt{17}$