Algebra Examples

$\frac{{(2 - 3^{2})}^{2} + \sqrt{81}}{10 - 6 \div 3}$

Step 1

Cancel the common factor of $6$ and $3$ .

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Step 1.1

Factor $3$ out of $6$ .

$\frac{{(2 - 3^{2})}^{2} + \sqrt{81}}{10 - 3 \cdot 2 \div 3}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3$ .

$\frac{{(2 - 3^{2})}^{2} + \sqrt{81}}{10 - 3 \cdot 2 \div 3 (1)}$

Step 1.2.2

Cancel the common factor.

$\frac{{(2 - 3^{2})}^{2} + \sqrt{81}}{10 - 3 \cdot 2 \div 3 \cdot 1}$

Step 1.2.3

Rewrite the expression.

$\frac{{(2 - 3^{2})}^{2} + \sqrt{81}}{10 - \frac{2}{1}}$

Step 1.2.4

Divide $2$ by $1$ .

$\frac{{(2 - 3^{2})}^{2} + \sqrt{81}}{10 - 1 \cdot 2}$

Step 2

Simplify the numerator.

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $3$ to the power of $2$ .

$\frac{{(2 - 1 \cdot 9)}^{2} + \sqrt{81}}{10 - 1 \cdot 2}$

Step 2.1.2

Multiply $- 1$ by $9$ .

$\frac{{(2 - 9)}^{2} + \sqrt{81}}{10 - 1 \cdot 2}$

Step 2.2

Subtract $9$ from $2$ .

$\frac{{(- 7)}^{2} + \sqrt{81}}{10 - 1 \cdot 2}$

Step 2.3

Raise $- 7$ to the power of $2$ .

$\frac{49 + \sqrt{81}}{10 - 1 \cdot 2}$

Step 2.4

Rewrite $81$ as $9^{2}$ .

$\frac{49 + \sqrt{9^{2}}}{10 - 1 \cdot 2}$

Step 2.5

Pull terms out from under the radical, assuming positive real numbers.

$\frac{49 + 9}{10 - 1 \cdot 2}$

Step 2.6

Add $49$ and $9$ .

$\frac{58}{10 - 1 \cdot 2}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $- 1$ by $2$ .

$\frac{58}{10 - 2}$

Step 3.2

Subtract $2$ from $10$ .

$\frac{58}{8}$

Step 4

Cancel the common factor of $58$ and $8$ .

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Step 4.1

Factor $2$ out of $58$ .

$\frac{2 (29)}{8}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $8$ .

$\frac{2 \cdot 29}{2 \cdot 4}$

Step 4.2.2

Cancel the common factor.

$\frac{2 \cdot 29}{2 \cdot 4}$

Step 4.2.3

Rewrite the expression.

$\frac{29}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{4}$

Decimal Form:

$7.25$

Mixed Number Form:

$7 \frac{1}{4}$