Simplify the Radical Expression ( square root of 10)^3

${(\sqrt{10})}^{3}$

Step 1

Rewrite ${\sqrt{10}}^{3}$ as ${(10^{3})}^{\frac{1}{2}}$ .

$\sqrt{10^{3}}$

Step 2

Raise $10$ to the power of $3$ .

$\sqrt{1000}$

Step 3

Rewrite $1000$ as $10^{2} \cdot 10$ .

Factor $100$ out of $1000$ .

$\sqrt{100 (10)}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 10}$

Step 4

Pull terms out from under the radical.

$| 10 | \sqrt{10}$

Step 5

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$10 \sqrt{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{10}$

Decimal Form:

$31.62277660 \dots$