which expression is equivalent to $sqrt{-108}-sqrt{-3}$?\n$5isqrt{3}$\n$6isqrt{3}$\n$7isqrt{3}$\n$8isqrt{3}$
which expression is equivalent to $sqrt{-108}-sqrt{-3}$?\n$5isqrt{3}$\n$6isqrt{3}$\n$7isqrt{3}$\n$8isqrt{3}$
Answer
Answer:
A. $5i\sqrt{3}$
Explanation:
Step1: Simplify $\sqrt{- 108}$
We know that $\sqrt{-a}=\sqrt{a}\times i$ for $a>0$. So, $\sqrt{-108}=\sqrt{108}\times i$. And $\sqrt{108}=\sqrt{36\times3}=6\sqrt{3}$, then $\sqrt{-108}=6i\sqrt{3}$.
Step2: Simplify $\sqrt{-3}$
$\sqrt{-3}=\sqrt{3}\times i = i\sqrt{3}$.
Step3: Calculate the difference
$\sqrt{-108}-\sqrt{-3}=6i\sqrt{3}-i\sqrt{3}=(6 - 1)i\sqrt{3}=5i\sqrt{3}$.