Learn how to solve problems step by step online. Find the limit of (x^6+5x^3)^(1/2)-x^3 as x approaches infinity. Factor the polynomial x^6+5x^3 by it's greatest common factor (GCF): x^{3}. The power of a product is equal to the product of it's factors raised to the same power. Simplify \sqrt{x^{3}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{1}{2}. Applying rationalisation.

Find the limit of (x^6+5x^3)^(1/2)-x^3 as x approaches infinity