Explanation:
The question involves dividing radicals
To resolve the question, we will follow the steps below
Step 1: Write the expression
[tex]\sqrt{50x^3}\div\sqrt{32x^2}[/tex]
Step 2: simplify the expression in parts and apply the laws
[tex]\begin{gathered} \sqrt{50x^3}=\sqrt{25\times2\times x^2\times x} \\ =\sqrt{25\times2\times x^2\times x}=\sqrt{5^2\times2\times x^2\times x}=\sqrt{5^2}\times\sqrt{x^2}\times\sqrt{2x} \end{gathered}[/tex]
Thus
[tex]\begin{gathered} \sqrt{50x^3}=\sqrt{5^2}\times\sqrt{x^2}\times\sqrt{2x}=5\times x\times\sqrt{2x} \\ Therefore \\ \sqrt{50x^3}=5x\sqrt{2x} \end{gathered}[/tex]
For the second part
[tex]\sqrt{32x^2}=\sqrt{16\times2\times x^2}[/tex]
simplifying further
[tex]\sqrt{16\times2\times x^2}=\sqrt{16}\times\sqrt{x^2}\times\sqrt{2}[/tex]
Hence, we have
[tex]\sqrt{16}\times\sqrt{x^2}\times\sqrt{2}=4\times x\times\sqrt{2}=4x\sqrt{2}[/tex]
Finally, we will combine the simplified terms, so that we will have
[tex]\sqrt{50x^3}\div\sqrt{32x^2}=5x\sqrt{2x}\div4x\sqrt{2}[/tex]
Hence, we will have
[tex]\frac{5x\sqrt{2x}}{4x\sqrt{2}}=\frac{5}{4}\times\frac{x}{x}\times\frac{\sqrt{2}}{\sqrt{2}}\times\frac{\sqrt{x}}{1}[/tex]
By canceling out the common parts, we will have the answer to be
[tex]\frac{5}{4}\sqrt{x}[/tex]
