Basic Math Examples

A = 3 \sqrt{11} + 5 \sqrt{44} - 3 \sqrt{99}

$A = 3 \sqrt{11} + 5 \sqrt{44} - 3 \sqrt{99}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

44

$44$ as

2^{2} \cdot 11

$2^{2} \cdot 11$ .

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Step 1.1.1

Factor

4

$4$ out of

44

$44$ .

A = 3 \sqrt{11} + 5 \sqrt{4 (11)} - 3 \sqrt{99}

$A = 3 \sqrt{11} + 5 \sqrt{4 (11)} - 3 \sqrt{99}$

Step 1.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

A = 3 \sqrt{11} + 5 \sqrt{2^{2} \cdot 11} - 3 \sqrt{99}

$A = 3 \sqrt{11} + 5 \sqrt{2^{2} \cdot 11} - 3 \sqrt{99}$

A = 3 \sqrt{11} + 5 \sqrt{2^{2} \cdot 11} - 3 \sqrt{99}

$A = 3 \sqrt{11} + 5 \sqrt{2^{2} \cdot 11} - 3 \sqrt{99}$

Step 1.2

Pull terms out from under the radical.

A = 3 \sqrt{11} + 5 (2 \sqrt{11}) - 3 \sqrt{99}

$A = 3 \sqrt{11} + 5 (2 \sqrt{11}) - 3 \sqrt{99}$

Step 1.3

Multiply

2

$2$ by

5

$5$ .

A = 3 \sqrt{11} + 10 \sqrt{11} - 3 \sqrt{99}

$A = 3 \sqrt{11} + 10 \sqrt{11} - 3 \sqrt{99}$

Step 1.4

Rewrite

99

$99$ as

3^{2} \cdot 11

$3^{2} \cdot 11$ .

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Step 1.4.1

Factor

9

$9$ out of

99

$99$ .

A = 3 \sqrt{11} + 10 \sqrt{11} - 3 \sqrt{9 (11)}

$A = 3 \sqrt{11} + 10 \sqrt{11} - 3 \sqrt{9 (11)}$

Step 1.4.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

A = 3 \sqrt{11} + 10 \sqrt{11} - 3 \sqrt{3^{2} \cdot 11}

$A = 3 \sqrt{11} + 10 \sqrt{11} - 3 \sqrt{3^{2} \cdot 11}$

A = 3 \sqrt{11} + 10 \sqrt{11} - 3 \sqrt{3^{2} \cdot 11}

$A = 3 \sqrt{11} + 10 \sqrt{11} - 3 \sqrt{3^{2} \cdot 11}$

Step 1.5

Pull terms out from under the radical.

A = 3 \sqrt{11} + 10 \sqrt{11} - 3 (3 \sqrt{11})

$A = 3 \sqrt{11} + 10 \sqrt{11} - 3 (3 \sqrt{11})$

Step 1.6

Multiply

3

$3$ by

- 3

$- 3$ .

A = 3 \sqrt{11} + 10 \sqrt{11} - 9 \sqrt{11}

$A = 3 \sqrt{11} + 10 \sqrt{11} - 9 \sqrt{11}$

A = 3 \sqrt{11} + 10 \sqrt{11} - 9 \sqrt{11}

$A = 3 \sqrt{11} + 10 \sqrt{11} - 9 \sqrt{11}$

Step 2

Simplify by adding terms.

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Step 2.1

Add

3 \sqrt{11}

$3 \sqrt{11}$ and

10 \sqrt{11}

$10 \sqrt{11}$ .

A = 13 \sqrt{11} - 9 \sqrt{11}

$A = 13 \sqrt{11} - 9 \sqrt{11}$

Step 2.2

Subtract

9 \sqrt{11}

$9 \sqrt{11}$ from

13 \sqrt{11}

$13 \sqrt{11}$ .

A = 4 \sqrt{11}

$A = 4 \sqrt{11}$

A = 4 \sqrt{11}

$A = 4 \sqrt{11}$

Step 3

The result can be shown in multiple forms.

Exact Form:

A = 4 \sqrt{11}

$A = 4 \sqrt{11}$

Decimal Form:

A = 13.26649916 \dots

$A = 13.26649916 \dots$