Simplify cube root of 189

$\sqrt[3]{189}$

Step 1

Rewrite $189$ as $3^{3} \cdot 7$ .

Factor $27$ out of $189$ .

$\sqrt[3]{27 (7)}$

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3} \cdot 7}$

$\sqrt[3]{3^{3} \cdot 7}$

Step 2

Pull terms out from under the radical.

$3 \sqrt[3]{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{7}$

Decimal Form:

$5.73879354 \dots$

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