Linear Algebra Examples

- \sqrt{68} \sqrt{407}

$- \sqrt{68} \sqrt{407}$

Step 1

Rewrite

68

$68$ as

2^{2} \cdot 17

$2^{2} \cdot 17$ .

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Step 1.1

Factor

4

$4$ out of

68

$68$ .

- \sqrt{4 (17)} \sqrt{407}

$- \sqrt{4 (17)} \sqrt{407}$

Step 1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

- \sqrt{2^{2} \cdot 17} \sqrt{407}

$- \sqrt{2^{2} \cdot 17} \sqrt{407}$

- \sqrt{2^{2} \cdot 17} \sqrt{407}

$- \sqrt{2^{2} \cdot 17} \sqrt{407}$

Step 2

Pull terms out from under the radical.

- (2 \sqrt{17}) \sqrt{407}

$- (2 \sqrt{17}) \sqrt{407}$

Step 3

Multiply

2

$2$ by

- 1

$- 1$ .

- 2 \sqrt{17} \sqrt{407}

$- 2 \sqrt{17} \sqrt{407}$

Step 4

Multiply

- 2 \sqrt{17} \sqrt{407}

$- 2 \sqrt{17} \sqrt{407}$ .

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Step 4.1

Combine using the product rule for radicals.

- 2 \sqrt{407 \cdot 17}

$- 2 \sqrt{407 \cdot 17}$

Step 4.2

Multiply

407

$407$ by

17

$17$ .

- 2 \sqrt{6919}

$- 2 \sqrt{6919}$

- 2 \sqrt{6919}

$- 2 \sqrt{6919}$

Step 5

The result can be shown in multiple forms.

Exact Form:

- 2 \sqrt{6919}

$- 2 \sqrt{6919}$

Decimal Form:

- 166.36105313 \dots

$- 166.36105313 \dots$

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

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