Evaluate 4 square root of 3* square root of 21

$4 \sqrt{3} \cdot \sqrt{21}$

Multiply $4 \sqrt{3} \sqrt{21}$ .

Combine using the product rule for radicals.

$4 \sqrt{21 \cdot 3}$

Multiply $21$ by $3$ .

$4 \sqrt{63}$

$4 \sqrt{63}$

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$4 \sqrt{9 (7)}$

Rewrite $9$ as $3^{2}$ .

$4 \sqrt{3^{2} \cdot 7}$

$4 \sqrt{3^{2} \cdot 7}$

Pull terms out from under the radical.

$4 (3 \sqrt{7})$

Multiply $3$ by $4$ .

$12 \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{7}$

Decimal Form:

$31.74901573 \dots$

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