Answer:
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{5\sqrt{10c^3} }{3d^3}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{\frac{250c^3}{9d^6}}[/tex]
Required
Simplify to the simplest form
We start by splitting the square root
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250c^3}}{\sqrt{9d^6}}[/tex]
Expand
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250 * c^3}}{\sqrt{9 * d^6}}[/tex]
Further Split the square root
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250} * \sqrt{c^3}}{\sqrt{9}*\sqrt{d^6}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250} * \sqrt{c^3}}{3*\sqrt{d^6}}[/tex]
From laws of indices;
[tex]\sqrt[n]{a^m} = a^{\frac{m}{n}}[/tex]
This implies that
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250} * \sqrt{c^3}}{3*{d^{\frac{6}{2}}}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250} * \sqrt{c^3}}{3*{d^3}}[/tex]
Expand 250 to 25 * 10
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{25 * 10} * \sqrt{c^3}}{3*{d^3}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{25}*\sqrt{10} * \sqrt{c^3}}{3*{d^3}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{5*\sqrt{10} * \sqrt{c^3}}{3*{d^3}}[/tex]
Combine the square roots
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{5*\sqrt{10*c^3} }{3*{d^3}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{5\sqrt{10c^3} }{3d^3}[/tex]
Solved
