Evaluate (2 square root of 24)(7 square root of 18)

$(2 \sqrt{24}) (7 \sqrt{18})$

Step 1

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$2 \sqrt{4 (6)} (7 \sqrt{18})$

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

$2 \sqrt{2^{2} \cdot 6} (7 \sqrt{18})$

$2 \sqrt{2^{2} \cdot 6} (7 \sqrt{18})$

Step 2

Pull terms out from under the radical.

$2 (2 \sqrt{6}) (7 \sqrt{18})$

Step 3

Multiply $2$ by $2$ .

$4 \sqrt{6} (7 \sqrt{18})$

Step 4

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$4 \sqrt{6} (7 \sqrt{9 (2)})$

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

$4 \sqrt{6} (7 \sqrt{3^{2} \cdot 2})$

$4 \sqrt{6} (7 \sqrt{3^{2} \cdot 2})$

Step 5

Pull terms out from under the radical.

$4 \sqrt{6} (7 (3 \sqrt{2}))$

Step 6

Multiply $3$ by $7$ .

$4 \sqrt{6} (21 \sqrt{2})$

Step 7

Multiply $4 \sqrt{6} (21 \sqrt{2})$ .

Multiply $21$ by $4$ .

$84 \sqrt{6} \sqrt{2}$

Combine using the product rule for radicals.

$84 \sqrt{2 \cdot 6}$

Multiply $2$ by $6$ .

$84 \sqrt{12}$

$84 \sqrt{12}$

Step 8

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

Factor $4$ out of $12$ .

$84 \sqrt{4 (3)}$

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

$84 \sqrt{2^{2} \cdot 3}$

$84 \sqrt{2^{2} \cdot 3}$

Step 9

Pull terms out from under the radical.

$84 (2 \sqrt{3})$

Step 10

Multiply $2$ by $84$ .

$168 \sqrt{3}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$168 \sqrt{3}$

Decimal Form:

$290.98453567 \dots$

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