Express each radical expression in simplest radical form.\sqrt[3]{56}

facas9 2021-09-22 Answered

Express each radical expression in simplest radical form.
\(\displaystyle\sqrt[3]{56}\)

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Expert Answer

Szeteib
Answered 2021-09-23 Author has 5277 answers

We have to express the given radical expression in simplest radical form:
\(\displaystyle\sqrt[3]{56}\)
We know the laws of exponents,
\(\displaystyle\sqrt[m]{a}={a}^{{{\frac{{{1}}}{{{m}}}}}}\)
\(\displaystyle{\left({a}^{{m}}\right)}^{{n}}={a}^{{{m}\times{n}}}\)
\(\displaystyle{\left({a}{b}\right)}^{{m}}={a}^{{m}}{b}^{{m}}\)
Applying above laws for the given expression, we get
\(\displaystyle\sqrt[3]{56}={\left({56}\right)}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle={\left({8}\times{7}\right)}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle={\left({2}\times{2}\times{2}\times{7}\right)}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle={\left({2}^{{3}}\times{7}\right)}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle={\left({2}^{{3}}\right)}^{{\frac{{{1}}}{{{3}}}}}{\left({7}\right)}^{{\frac{{1}}{{3}}}}\)
\(\displaystyle={2}\sqrt[3]{7}\)
Hence, simplest form of the radical expression is \(\displaystyle={2}\sqrt[3]{7}\)

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