Basic Math Examples

$y = \frac{- 6 + \sqrt{32}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.1.1

Factor $16$ out of $32$ .

$y = \frac{- 6 + \sqrt{16 (2)}}{2}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$y = \frac{- 6 + \sqrt{4^{2} \cdot 2}}{2}$

$y = \frac{- 6 + \sqrt{4^{2} \cdot 2}}{2}$

Step 1.2

Pull terms out from under the radical.

$y = \frac{- 6 + 4 \sqrt{2}}{2}$

$y = \frac{- 6 + 4 \sqrt{2}}{2}$

Step 2

Cancel the common factor of $- 6 + 4 \sqrt{2}$ and $2$ .

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Step 2.1

Factor $2$ out of $- 6$ .

$y = \frac{2 \cdot - 3 + 4 \sqrt{2}}{2}$

Step 2.2

Factor $2$ out of $4 \sqrt{2}$ .

$y = \frac{2 \cdot - 3 + 2 (2 \sqrt{2})}{2}$

Step 2.3

Factor $2$ out of $2 (- 3) + 2 (2 \sqrt{2})$ .

$y = \frac{2 (- 3 + 2 \sqrt{2})}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$y = \frac{2 (- 3 + 2 \sqrt{2})}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$y = \frac{2 (- 3 + 2 \sqrt{2})}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$y = \frac{- 3 + 2 \sqrt{2}}{1}$

Step 2.4.4

Divide $- 3 + 2 \sqrt{2}$ by $1$ .

$y = - 3 + 2 \sqrt{2}$

$y = - 3 + 2 \sqrt{2}$

$y = - 3 + 2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = - 3 + 2 \sqrt{2}$

Decimal Form:

$y = - 0.17157287 \dots$

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