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Answer:
[tex]\frac{3\sqrt{2x}}{5}[/tex]
Step-by-step explanation:
Starting point:
[tex]\frac{\sqrt{72x^3}}{50x^2}\\[/tex]
1) Factor it by Prime Factor Method 72 and 50
[tex]72|2\\ 36|2\\ 18|2\\ 9|3\\3|3\\ 1\\ 72=2^2*3^2*2[/tex]
[tex]50|2\\ 25|5\\ 5|5\\ 1\\ 50=2*5^2[/tex]
2) Plug it in the factored form. Every exponent to the second power will be outside the radical, so its roots.
[tex]\frac{\sqrt{72x^2*x}}{50x^2}=\frac{6x\sqrt{2x}}{5x\sqrt{2}}=\frac{6\sqrt{x}}{5\sqrt{2}}[/tex]
3) Rationalize it multiplying by the radical, so that you can eliminate the square root on the denominator.
[tex]\frac{6\sqrt{x}}{5\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{6\sqrt{2x}}{10}=\frac{3\sqrt{2x}}{5}[/tex]