Pre-Algebra Examples

$(\sqrt{5}) (\sqrt[3]{10})$

Step 1

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

Tap for more steps...

Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$5^{\frac{1}{2}} \sqrt[3]{10}$

Step 1.2

Rewrite $5^{\frac{1}{2}}$ as $5^{\frac{3}{6}}$ .

$5^{\frac{3}{6}} \sqrt[3]{10}$

Step 1.3

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

$\sqrt[6]{5^{3}} \sqrt[3]{10}$

Step 1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{10}$ as $10^{\frac{1}{3}}$ .

$\sqrt[6]{5^{3}} \cdot 10^{\frac{1}{3}}$

Step 1.5

Rewrite $10^{\frac{1}{3}}$ as $10^{\frac{2}{6}}$ .

$\sqrt[6]{5^{3}} \cdot 10^{\frac{2}{6}}$

Step 1.6

Rewrite $10^{\frac{2}{6}}$ as $\sqrt[6]{10^{2}}$ .

$\sqrt[6]{5^{3}} \sqrt[6]{10^{2}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[6]{5^{3} \cdot 10^{2}}$

Step 3

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

$\sqrt[6]{125 \cdot 10^{2}}$

Step 4

Raise $10$ to the power of $2$ .

$\sqrt[6]{125 \cdot 100}$

Step 5

Multiply $125$ by $100$ .

$\sqrt[6]{12500}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt[6]{12500}$

Decimal Form:

$4.81746241 \dots$