Simplify: {square root of {72 x^3} / {8 x}.

First, we can simplify the square root by breaking down 72 and x^3 into their prime factors. 72 = 2^3 * 3^2 x^3 = x^2 * x So, the square root of 72x^3 becomes: sqrt(72x^3) = sqrt(2^3 * 3^2 * x^2 * x) = sqrt(2^3) * sqrt(3^2) * sqrt(x^2) * sqrt(x) = 2 * 3 * x * sqrt(x) = 6x * sqrt(x) Now, we can substitute the simplified version of the square root into the original expression: {eq}\displaystyle dfrac {sqrt{72 x^3}} {8 x} = dfrac{6xsqrt{x}}{8x} = dfrac{3sqrt{x}}{4} {/eq} Therefore, the simplified expression is 3/4 times the square root of x.