Basic Math Examples

\sqrt{- 14} \cdot \sqrt{- 17}

$\sqrt{- 14} \cdot \sqrt{- 17}$

Step 1

Rewrite

$- 14$ as

$- 1 (14)$ .

$\sqrt{- 1 (14)} \cdot \sqrt{- 17}$

Step 2

Rewrite

$\sqrt{- 1 (14)}$ as

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

$\sqrt{- 1} \cdot \sqrt{14} \cdot \sqrt{- 17}$

Step 3

Rewrite

$\sqrt{- 1}$ as

$i$ .

$i \cdot \sqrt{14} \cdot \sqrt{- 17}$

Step 4

Rewrite

$- 17$ as

$- 1 (17)$ .

$i \cdot \sqrt{14} \cdot \sqrt{- 1 (17)}$

Step 5

Rewrite

$\sqrt{- 1 (17)}$ as

$\sqrt{- 1} \cdot \sqrt{17}$ .

$i \cdot \sqrt{14} \cdot (\sqrt{- 1} \cdot \sqrt{17})$

Step 6

Rewrite

$\sqrt{- 1}$ as

$i$ .

$i \cdot \sqrt{14} \cdot (i \cdot \sqrt{17})$

Step 7

Multiply

$i \sqrt{14} (i \sqrt{17})$ .

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Step 7.1

Raise

$i$ to the power of

$1$ .

$i^{1} i \sqrt{14} \sqrt{17}$

Step 7.2

Raise

$i$ to the power of

$1$ .

$i^{1} i^{1} \sqrt{14} \sqrt{17}$

Step 7.3

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$i^{1 + 1} \sqrt{14} \sqrt{17}$

Step 7.4

Add

$1$ and

$1$ .

$i^{2} \sqrt{14} \sqrt{17}$

Step 7.5

Combine using the product rule for radicals.

$i^{2} \sqrt{17 \cdot 14}$

Step 7.6

Multiply

$17$ by

$14$ .

$i^{2} \sqrt{238}$

$i^{2} \sqrt{238}$

Step 8

Rewrite

$i^{2}$ as

$- 1$ .

$- 1 \sqrt{238}$

Step 9

Rewrite

$- 1 \sqrt{238}$ as

$- \sqrt{238}$ .

$- \sqrt{238}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{238}$

Decimal Form:

$- 15.42724862 \dots$

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