Algebra Examples

$(12 \sqrt{12 d^{4}}) (7 \sqrt{4 d^{4}})$

Step 1

Rewrite $12 d^{4}$ as ${(2 d^{2})}^{2} \cdot 3$ .

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Step 1.1

Factor $4$ out of $12$ .

$12 \sqrt{4 (3) d^{4}} (7 \sqrt{4 d^{4}})$

Step 1.2

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

$12 \sqrt{2^{2} \cdot 3 d^{4}} (7 \sqrt{4 d^{4}})$

Step 1.3

Rewrite $d^{4}$ as ${(d^{2})}^{2}$ .

$12 \sqrt{2^{2} \cdot 3 {(d^{2})}^{2}} (7 \sqrt{4 d^{4}})$

Step 1.4

Move $3$ .

$12 \sqrt{2^{2} {(d^{2})}^{2} \cdot 3} (7 \sqrt{4 d^{4}})$

Step 1.5

Rewrite $2^{2} {(d^{2})}^{2}$ as ${(2 d^{2})}^{2}$ .

$12 \sqrt{{(2 d^{2})}^{2} \cdot 3} (7 \sqrt{4 d^{4}})$

Step 2

Pull terms out from under the radical.

$12 (2 d^{2} \sqrt{3}) (7 \sqrt{4 d^{4}})$

Step 3

Multiply $2$ by $12$ .

$24 (d^{2} \sqrt{3}) (7 \sqrt{4 d^{4}})$

Step 4

Rewrite $4 d^{4}$ as ${(2 d^{2})}^{2}$ .

$24 d^{2} \sqrt{3} (7 \sqrt{{(2 d^{2})}^{2}})$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$24 d^{2} \sqrt{3} (7 (2 d^{2}))$

Step 6

Multiply $d^{2}$ by $d^{2}$ by adding the exponents.

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Step 6.1

Move $d^{2}$ .

$24 (d^{2} d^{2}) \sqrt{3} (7 \cdot (2))$

Step 6.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$24 d^{2 + 2} \sqrt{3} (7 \cdot (2))$

Step 6.3

Add $2$ and $2$ .

$24 d^{4} \sqrt{3} (7 \cdot (2))$

Step 7

Multiply $7$ by $2$ .

$24 d^{4} \sqrt{3} \cdot 14$

Step 8

Multiply $14$ by $24$ .

$336 d^{4} \sqrt{3}$