Simplify the Radical Expression ( square root of 3)/( cube root of 3)

$\frac{\sqrt{3}}{\sqrt[3]{3}}$

Multiply $\frac{\sqrt{3}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$\frac{\sqrt{3}}{\sqrt[3]{3}} \cdot \frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{\sqrt[3]{3} {\sqrt[3]{3}}^{2}}$

Raise $\sqrt[3]{3}$ to the power of $1$ .

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1} {\sqrt[3]{3}}^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{3}}$

Rewrite ${\sqrt[3]{3}}^{3}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{3}$ as $3^{\frac{1}{3}}$ .

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{{(3^{\frac{1}{3}})}^{3}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{3^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{3^{1}}$

Evaluate the exponent.

$\frac{\sqrt{3} {\sqrt[3]{3}}^{2}}{3}$

Simplify the numerator.

Rewrite ${\sqrt[3]{3}}^{2}$ as ${(3^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt{3} \sqrt[3]{3^{2}}}{3}$

Raise $3$ to the power of $2$ .

$\frac{\sqrt{3} \sqrt[3]{9}}{3}$

Simplify the numerator.

Rewrite the expression using the least common index of $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{3^{\frac{1}{2}} \sqrt[3]{9}}{3}$

Rewrite $3^{\frac{1}{2}}$ as $3^{\frac{3}{6}}$ .

$\frac{3^{\frac{3}{6}} \sqrt[3]{9}}{3}$

Rewrite $3^{\frac{3}{6}}$ as $\sqrt[6]{3^{3}}$ .

$\frac{\sqrt[6]{3^{3}} \sqrt[3]{9}}{3}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9}$ as $9^{\frac{1}{3}}$ .

$\frac{\sqrt[6]{3^{3}} \cdot 9^{\frac{1}{3}}}{3}$

Rewrite $9^{\frac{1}{3}}$ as $9^{\frac{2}{6}}$ .

$\frac{\sqrt[6]{3^{3}} \cdot 9^{\frac{2}{6}}}{3}$

Rewrite $9^{\frac{2}{6}}$ as $\sqrt[6]{9^{2}}$ .

$\frac{\sqrt[6]{3^{3}} \sqrt[6]{9^{2}}}{3}$

Combine using the product rule for radicals.

$\frac{\sqrt[6]{3^{3} \cdot 9^{2}}}{3}$

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt[6]{3^{3} \cdot {(3^{2})}^{2}}}{3}$

Multiply the exponents in ${(3^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt[6]{3^{3} \cdot 3^{2 \cdot 2}}}{3}$

Multiply $2$ by $2$ .

$\frac{\sqrt[6]{3^{3} \cdot 3^{4}}}{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt[6]{3^{3 + 4}}}{3}$

Add $3$ and $4$ .

$\frac{\sqrt[6]{3^{7}}}{3}$

Simplify the numerator.

Raise $3$ to the power of $7$ .

$\frac{\sqrt[6]{2187}}{3}$

Rewrite $2187$ as $3^{6} \cdot 3$ .

Factor $729$ out of $2187$ .

$\frac{\sqrt[6]{729 (3)}}{3}$

Rewrite $729$ as $3^{6}$ .

$\frac{\sqrt[6]{3^{6} \cdot 3}}{3}$

Pull terms out from under the radical.

$\frac{| 3 | \sqrt[6]{3}}{3}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{3 \sqrt[6]{3}}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \sqrt[6]{3}}{3}$

Divide $\sqrt[6]{3}$ by $1$ .

$\sqrt[6]{3}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[6]{3}$

Decimal Form:

$1.20093695 \dots$

Simplify the Radical Expression ( square root of 3)/( cube root of 3)

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