Divide ( cube root of 3)÷( square root of 3)

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

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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

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

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

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 4

Simplify the numerator.

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

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

$\frac{3^{\frac{1}{3}} \sqrt{3}}{3}$

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

$\frac{3^{\frac{2}{6}} \sqrt{3}}{3}$

Rewrite $3^{\frac{2}{6}}$ as $\sqrt[6]{3^{2}}$ .

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

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

$\frac{\sqrt[6]{3^{2}} \cdot 3^{\frac{1}{2}}}{3}$

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

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

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

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

Combine using the product rule for radicals.

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

Multiply $3^{2}$ by $3^{3}$ by adding the exponents.

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

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

Add $2$ and $3$ .

$\frac{\sqrt[6]{3^{5}}}{3}$

Step 5

Raise $3$ to the power of $5$ .

$\frac{\sqrt[6]{243}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[6]{243}}{3}$

Decimal Form:

$0.83268317 \dots$

Divide ( cube root of 3)÷( square root of 3)

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