Express each radical expression in simplest radical form. 4\sqrt{52x^3y^2

bobbie71G 2021-09-17 Answered
Express each radical expression in simplest radical form.
\(\displaystyle{4}\sqrt{{{52}{x}^{{3}}{y}^{{2}}}}\)

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Expert Answer

Talisha
Answered 2021-09-18 Author has 14332 answers
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,
\(\displaystyle\sqrt{{{a}\times{a}}}={a}\)
Simplifying the given radical expression,
\(\displaystyle{4}\sqrt{{{53}{x}^{{3}}{y}^{{2}}}}={4}\sqrt{{{13}\times{4}{x}^{{3}}{y}^{{2}}}}\)
\(\displaystyle={4}\sqrt{{{13}\times{2}\times{2}\times{x}\times{x}\times{x}\times{y}\times{y}}}\)
\(\displaystyle={4}\times{2}\times{x}\times{y}\sqrt{{{13}\times{x}}}\)
\(\displaystyle={8}{x}{y}\sqrt{{{13}{x}}}\)
Hence, simplified form of the given radical expression in simplest radical form is \(\displaystyle{8}{x}{y}\sqrt{{{13}{x}}}\)
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