Mean absolute gap between two independent normals

Let $X$ and $Y$ be independent normal variables, where $X$ is standard normal and $Y$ has mean $0$ and variance $4$. The expected absolute difference $\mathbb{E}\,|Y-X|$ can be written as $\left(\tfrac{K}{\pi}\right)^b$ with $K$ and $b$ rational. Find $bK$.

$5$. The difference $Y-X$ is normal with mean $0$ and variance $1+4=5$. For $W\sim N(0,\sigma^2)$, $\mathbb{E}|W|=\sigma\sqrt{2/\pi}$, so the answer is $\sqrt{5}\sqrt{2/\pi}=(10/\pi)^{1/2}$, giving $K=10$, $b=\tfrac12$ and $bK=5$.