$$\displaystyle{4}\sqrt{{{52}{x}^{{3}}{y}^{{2}}}}$$

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Talisha
We have to express the given radical expression in simplest radical form:
$$\displaystyle{4}\sqrt{{{52}{x}^{{3}}{y}^{{2}}}}$$
We know the exponents rule,
$$\displaystyle\sqrt{{{a}\times{a}}}={a}$$
$$\displaystyle{4}\sqrt{{{53}{x}^{{3}}{y}^{{2}}}}={4}\sqrt{{{13}\times{4}{x}^{{3}}{y}^{{2}}}}$$
$$\displaystyle={4}\sqrt{{{13}\times{2}\times{2}\times{x}\times{x}\times{x}\times{y}\times{y}}}$$
$$\displaystyle={4}\times{2}\times{x}\times{y}\sqrt{{{13}\times{x}}}$$
$$\displaystyle={8}{x}{y}\sqrt{{{13}{x}}}$$
Hence, simplified form of the given radical expression in simplest radical form is $$\displaystyle{8}{x}{y}\sqrt{{{13}{x}}}$$