Basic Math Examples

$(\sqrt{121} + \sqrt{81}) + 4 + {(5 - 3)}^{2} \cdot 2$

Step 1

Simplify each term.

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Step 1.1

Rewrite $121$ as $11^{2}$ .

$\sqrt{11^{2}} + \sqrt{81} + 4 + {(5 - 3)}^{2} \cdot 2$

Step 1.2

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

$11 + \sqrt{81} + 4 + {(5 - 3)}^{2} \cdot 2$

Step 1.3

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

$11 + \sqrt{9^{2}} + 4 + {(5 - 3)}^{2} \cdot 2$

Step 1.4

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

$11 + 9 + 4 + {(5 - 3)}^{2} \cdot 2$

Step 1.5

Subtract $3$ from $5$ .

$11 + 9 + 4 + 2^{2} \cdot 2$

Step 1.6

Multiply $2^{2}$ by $2$ by adding the exponents.

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Step 1.6.1

Multiply $2^{2}$ by $2$ .

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Step 1.6.1.1

Raise $2$ to the power of $1$ .

$11 + 9 + 4 + 2^{2} \cdot 2^{1}$

Step 1.6.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$11 + 9 + 4 + 2^{2 + 1}$

Step 1.6.2

Add $2$ and $1$ .

$11 + 9 + 4 + 2^{3}$

Step 1.7

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

$11 + 9 + 4 + 8$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $11$ and $9$ .

$20 + 4 + 8$

Step 2.2

Add $20$ and $4$ .

$24 + 8$

Step 2.3

Add $24$ and $8$ .

$32$