What is sqrt(3)\times \sqrt[3]{3} ?

The solution to sqrt(3)\times \sqrt[3]{3} is \sqrt[6]{3^5}

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simplify sqrt(3)\times \sqrt[3]{3}

simplify

Solution steps

Apply radical rule:

a = a^{\frac{1}{2}}

3 = 3^{\frac{1}{2}}

Apply radical rule:

= 3^{\frac{1}{2}} \cdot 3^{\frac{1}{3}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3^{\frac{1}{2}} \cdot 3^{\frac{1}{3}} = 3^{\frac{1}{2} + \frac{1}{3}}

= 3^{\frac{1}{2} + \frac{1}{3}}

\frac{1}{2} + \frac{1}{3} = \frac{5}{6}

= 3^{\frac{5}{6}}

(1 6^{5})^{\frac{1}{2}}

\frac{147}{100}

+ 3 x y + 12 x - 2 y - 8

10 \div \frac{1}{4}

\frac{x ^{2} - 49}{2 x ^{4} - 14 x ^{3}}

What is sqrt(3)\times \sqrt[3]{3} ?
The solution to sqrt(3)\times \sqrt[3]{3} is \sqrt[6]{3^5}