To obtain the square root of 16x^36, the coefficient portion (16) will not present any problems since 16 is a perfect square. However, for a variable with an exponent, the exponent is to be multiplied by 1/2 since the square root symbol is equal to raising the term inside to the power of 1/2. This is shown below:
sqrt (16 x^36) = 4 * x^36(1/2) = 4 * x^18
Therefore, the correct answer is 4x^18.