Algebra Examples

$\sqrt{- 14} \cdot \sqrt{18}$

Step 1

Rewrite $- 14$ as $- 1 (14)$ .

$\sqrt{- 1 (14)} \cdot \sqrt{18}$

Step 2

Rewrite $\sqrt{- 1 (14)}$ as $\sqrt{- 1} \cdot \sqrt{14}$ .

$\sqrt{- 1} \cdot \sqrt{14} \cdot \sqrt{18}$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$i \cdot \sqrt{14} \cdot \sqrt{18}$

Step 4

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

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Step 4.1

Factor $9$ out of $18$ .

$i \sqrt{14} \cdot \sqrt{9 (2)}$

Step 4.2

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

$i \sqrt{14} \cdot \sqrt{3^{2} \cdot 2}$

$i \sqrt{14} \cdot \sqrt{3^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$i \sqrt{14} \cdot (3 \sqrt{2})$

Step 6

Multiply $i \sqrt{14} (3 \sqrt{2})$ .

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Step 6.1

Combine using the product rule for radicals.

$i (3 \sqrt{14 \cdot 2})$

Step 6.2

Multiply $14$ by $2$ .

$i (3 \sqrt{28})$

$i (3 \sqrt{28})$

Step 7

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 7.1

Factor $4$ out of $28$ .

$i (3 \sqrt{4 (7)})$

Step 7.2

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

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

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

Step 8

Pull terms out from under the radical.

$i (3 (2 \sqrt{7}))$

Step 9

Simplify the expression.

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Step 9.1

Multiply $2$ by $3$ .

$i (6 \sqrt{7})$

Step 9.2

Move $6$ to the left of $i$ .

$6 i \sqrt{7}$

$6 i \sqrt{7}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$