Basic Math Examples

$\sqrt{7 d} \cdot \sqrt{8 d}$

Step 1

Rewrite $8 d$ as $2^{2} \cdot (2 d)$ .

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Step 1.1

Factor $4$ out of $8$ .

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

Step 1.2

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

$\sqrt{7 d} \cdot \sqrt{2^{2} \cdot 2 d}$

Step 1.3

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$\sqrt{7 d} \cdot (2 \sqrt{2 d})$

Step 3

Rewrite using the commutative property of multiplication.

$2 \sqrt{7 d} \sqrt{2 d}$

Step 4

Multiply $2 \sqrt{7 d} \sqrt{2 d}$ .

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Step 4.1

Combine using the product rule for radicals.

$2 \sqrt{2 d (7 d)}$

Step 4.2

Multiply $7$ by $2$ .

$2 \sqrt{14 d \cdot d}$

Step 4.3

Raise $d$ to the power of $1$ .

$2 \sqrt{14 (d^{1} d)}$

Step 4.4

Raise $d$ to the power of $1$ .

$2 \sqrt{14 (d^{1} d^{1})}$

Step 4.5

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

$2 \sqrt{14 d^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$2 \sqrt{14 d^{2}}$

Step 5

Reorder $14$ and $d^{2}$ .

$2 \sqrt{d^{2} \cdot 14}$

Step 6

Pull terms out from under the radical.

$2 d \sqrt{14}$