Algebra Examples

$5^{\frac{1}{2}} + 10 {(125)}^{\frac{1}{2}}$

Step 1

Remove parentheses.

$5^{\frac{1}{2}} + 10 \cdot 125^{\frac{1}{2}}$

Step 2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{5^{1}} + 10 \cdot 125^{\frac{1}{2}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{5^{1}} + 10 \cdot \sqrt{125^{1}}$

Step 4

Anything raised to $1$ is the base itself.

$\sqrt{5} + 10 \cdot \sqrt{125^{1}}$

Step 5

Anything raised to $1$ is the base itself.

$\sqrt{5} + 10 \cdot \sqrt{125}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5} + 10 \cdot \sqrt{125}$

Decimal Form:

$114.03946685 \dots$