The smallest meaningful measure of length is called the Planck constant, and is defined in terms of three fundamental constants in nature: the speed of light $c = 3.00 \times 10^8 \textrm{ m/s}$, the gravitational constant $G = 6.67 \times 10^{-11} \textrm{ m}^3\textrm{/kg.s}^2$, and Planck’s constant $h = 6.63 \times 10^{-34} \textrm{ kg.m}^2\textrm{/s}$. The Planck length $l_P$ is given by the following combination of these three constants:
\begin{equation}
\large l_P = \sqrt{\dfrac{Gh}{c^3}}.
\end{equation}

Show that the dimensions of $l_P$ are length [L], and find the order of magnitude of $l_P$. [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are "strings" with lengths on the order of the Planck length, $10^{-35} \textrm{ m}$. These theories also suggest that the "Big Bang," with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]