Pre-Algebra Examples

$\sqrt[3]{\frac{375}{4}}$

Step 1

Rewrite $\sqrt[3]{\frac{375}{4}}$ as $\frac{\sqrt[3]{375}}{\sqrt[3]{4}}$ .

$\frac{\sqrt[3]{375}}{\sqrt[3]{4}}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $375$ as $5^{3} \cdot 3$ .

Tap for more steps...

Step 2.1.1

Factor $125$ out of $375$ .

$\frac{\sqrt[3]{125 (3)}}{\sqrt[3]{4}}$

Step 2.1.2

Rewrite $125$ as $5^{3}$ .

$\frac{\sqrt[3]{5^{3} \cdot 3}}{\sqrt[3]{4}}$

Step 2.2

Pull terms out from under the radical.

$\frac{5 \sqrt[3]{3}}{\sqrt[3]{4}}$

Step 3

Multiply $\frac{5 \sqrt[3]{3}}{\sqrt[3]{4}}$ by $\frac{{\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{2}}$ .

$\frac{5 \sqrt[3]{3}}{\sqrt[3]{4}} \cdot \frac{{\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{2}}$

Step 4

Combine and simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $\frac{5 \sqrt[3]{3}}{\sqrt[3]{4}}$ by $\frac{{\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{2}}$ .

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{\sqrt[3]{4} {\sqrt[3]{4}}^{2}}$

Step 4.2

Raise $\sqrt[3]{4}$ to the power of $1$ .

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{1} {\sqrt[3]{4}}^{2}}$

Step 4.3

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

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{1 + 2}}$

Step 4.4

Add $1$ and $2$ .

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{3}}$

Step 4.5

Rewrite ${\sqrt[3]{4}}^{3}$ as $4$ .

Tap for more steps...

Step 4.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4}$ as $4^{\frac{1}{3}}$ .

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{{(4^{\frac{1}{3}})}^{3}}$

Step 4.5.2

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

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{4^{\frac{1}{3} \cdot 3}}$

Step 4.5.3

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

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{4^{\frac{3}{3}}}$

Step 4.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.5.4.1

Cancel the common factor.

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{4^{\frac{3}{3}}}$

Step 4.5.4.2

Rewrite the expression.

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{4^{1}}$

Step 4.5.5

Evaluate the exponent.

$\frac{5 \sqrt[3]{3} {\sqrt[3]{4}}^{2}}{4}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Rewrite ${\sqrt[3]{4}}^{2}$ as $\sqrt[3]{4^{2}}$ .

$\frac{5 \sqrt[3]{3} \sqrt[3]{4^{2}}}{4}$

Step 5.2

Raise $4$ to the power of $2$ .

$\frac{5 \sqrt[3]{3} \sqrt[3]{16}}{4}$

Step 5.3

Rewrite $16$ as $2^{3} \cdot 2$ .

Tap for more steps...

Step 5.3.1

Factor $8$ out of $16$ .

$\frac{5 \sqrt[3]{3} \sqrt[3]{8 (2)}}{4}$

Step 5.3.2

Rewrite $8$ as $2^{3}$ .

$\frac{5 \sqrt[3]{3} \sqrt[3]{2^{3} \cdot 2}}{4}$

Step 5.4

Pull terms out from under the radical.

$\frac{5 \sqrt[3]{3} \cdot 2 \sqrt[3]{2}}{4}$

Step 5.5

Combine exponents.

Tap for more steps...

Step 5.5.1

Multiply $2$ by $5$ .

$\frac{10 \sqrt[3]{3} \sqrt[3]{2}}{4}$

Step 5.5.2

Combine using the product rule for radicals.

$\frac{10 \sqrt[3]{2 \cdot 3}}{4}$

Step 5.5.3

Multiply $2$ by $3$ .

$\frac{10 \sqrt[3]{6}}{4}$

Step 6

Cancel the common factor of $10$ and $4$ .

Tap for more steps...

Step 6.1

Factor $2$ out of $10 \sqrt[3]{6}$ .

$\frac{2 (5 \sqrt[3]{6})}{4}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $2$ out of $4$ .

$\frac{2 (5 \sqrt[3]{6})}{2 (2)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (5 \sqrt[3]{6})}{2 \cdot 2}$

Step 6.2.3

Rewrite the expression.

$\frac{5 \sqrt[3]{6}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt[3]{6}}{2}$

Decimal Form:

$4.54280148 \dots$