Simplify ( square root of 5)^3

${(\sqrt{5})}^{3}$

Step 1

Rewrite ${\sqrt{5}}^{3}$ as $\sqrt{5^{3}}$ .

$\sqrt{5^{3}}$

Step 2

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

$\sqrt{125}$

Step 3

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5)}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 5}$

$\sqrt{5^{2} \cdot 5}$

Step 4

Pull terms out from under the radical.

$5 \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{5}$

Decimal Form:

$11.18033988 \dots$

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