Basic Math Examples

$(\sqrt{99} + 2) (\sqrt{44} + 12)$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $99$ as $3^{2} \cdot 11$ .

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Step 1.1.1.1

Factor $9$ out of $99$ .

$(\sqrt{9 (11)} + 2) (\sqrt{44} + 12)$

Step 1.1.1.2

Rewrite $9$ as $3^{2}$ .

$(\sqrt{3^{2} \cdot 11} + 2) (\sqrt{44} + 12)$

Step 1.1.2

Pull terms out from under the radical.

$(3 \sqrt{11} + 2) (\sqrt{44} + 12)$

Step 1.2

Simplify each term.

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Step 1.2.1

Rewrite $44$ as $2^{2} \cdot 11$ .

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Step 1.2.1.1

Factor $4$ out of $44$ .

$(3 \sqrt{11} + 2) (\sqrt{4 (11)} + 12)$

Step 1.2.1.2

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

$(3 \sqrt{11} + 2) (\sqrt{2^{2} \cdot 11} + 12)$

Step 1.2.2

Pull terms out from under the radical.

$(3 \sqrt{11} + 2) (2 \sqrt{11} + 12)$

Step 2

Expand $(3 \sqrt{11} + 2) (2 \sqrt{11} + 12)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$3 \sqrt{11} (2 \sqrt{11} + 12) + 2 (2 \sqrt{11} + 12)$

Step 2.2

Apply the distributive property.

$3 \sqrt{11} (2 \sqrt{11}) + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11} + 12)$

Step 2.3

Apply the distributive property.

$3 \sqrt{11} (2 \sqrt{11}) + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $3 \sqrt{11} (2 \sqrt{11})$ .

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Step 3.1.1.1

Multiply $2$ by $3$ .

$6 \sqrt{11} \sqrt{11} + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.1.2

Raise $\sqrt{11}$ to the power of $1$ .

$6 ({\sqrt{11}}^{1} \sqrt{11}) + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.1.3

Raise $\sqrt{11}$ to the power of $1$ .

$6 ({\sqrt{11}}^{1} {\sqrt{11}}^{1}) + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.1.4

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

$6 {\sqrt{11}}^{1 + 1} + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.1.5

Add $1$ and $1$ .

$6 {\sqrt{11}}^{2} + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.2

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

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Step 3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$6 {(11^{\frac{1}{2}})}^{2} + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$6 \cdot 11^{\frac{1}{2} \cdot 2} + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.2.3

Combine $\frac{1}{2}$ and $2$ .

$6 \cdot 11^{\frac{2}{2}} + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.2.4

Cancel the common factor of $2$ .

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Step 3.1.2.4.1

Cancel the common factor.

$6 \cdot 11^{\frac{2}{2}} + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.2.4.2

Rewrite the expression.

$6 \cdot 11^{1} + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.2.5

Evaluate the exponent.

$6 \cdot 11 + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.3

Multiply $6$ by $11$ .

$66 + 3 \sqrt{11} \cdot 12 + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.4

Multiply $12$ by $3$ .

$66 + 36 \sqrt{11} + 2 (2 \sqrt{11}) + 2 \cdot 12$

Step 3.1.5

Multiply $2$ by $2$ .

$66 + 36 \sqrt{11} + 4 \sqrt{11} + 2 \cdot 12$

Step 3.1.6

Multiply $2$ by $12$ .

$66 + 36 \sqrt{11} + 4 \sqrt{11} + 24$

Step 3.2

Add $66$ and $24$ .

$90 + 36 \sqrt{11} + 4 \sqrt{11}$

Step 3.3

Add $36 \sqrt{11}$ and $4 \sqrt{11}$ .

$90 + 40 \sqrt{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$90 + 40 \sqrt{11}$

Decimal Form:

$222.66499161 \dots$