Evaluate (3 square root of 12)(2 square root of 21)

$(3 \sqrt{12}) (2 \sqrt{21})$

Step 1

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$3 \sqrt{4 (3)} (2 \sqrt{21})$

Rewrite $4$ as $2^{2}$ .

$3 \sqrt{2^{2} \cdot 3} (2 \sqrt{21})$

$3 \sqrt{2^{2} \cdot 3} (2 \sqrt{21})$

Step 2

Pull terms out from under the radical.

$3 (2 \sqrt{3}) (2 \sqrt{21})$

Step 3

Multiply $2$ by $3$ .

$6 \sqrt{3} (2 \sqrt{21})$

Step 4

Multiply $6 \sqrt{3} (2 \sqrt{21})$ .

Multiply $2$ by $6$ .

$12 \sqrt{3} \sqrt{21}$

Combine using the product rule for radicals.

$12 \sqrt{21 \cdot 3}$

Multiply $21$ by $3$ .

$12 \sqrt{63}$

$12 \sqrt{63}$

Step 5

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

Factor $9$ out of $63$ .

$12 \sqrt{9 (7)}$

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

$12 \sqrt{3^{2} \cdot 7}$

$12 \sqrt{3^{2} \cdot 7}$

Step 6

Pull terms out from under the radical.

$12 (3 \sqrt{7})$

Step 7

Multiply $3$ by $12$ .

$36 \sqrt{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$36 \sqrt{7}$

Decimal Form:

$95.24704719 \dots$

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