Basic Math Examples

$4 \sqrt{8} + 5 \sqrt{32} - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$4 \sqrt{4 (2)} + 5 \sqrt{32} - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1.1.2

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

$4 \sqrt{2^{2} \cdot 2} + 5 \sqrt{32} - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1.2

Pull terms out from under the radical.

$4 (2 \sqrt{2}) + 5 \sqrt{32} - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1.3

Multiply $2$ by $4$ .

$8 \sqrt{2} + 5 \sqrt{32} - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1.4

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

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Step 1.4.1

Factor $16$ out of $32$ .

$8 \sqrt{2} + 5 \sqrt{16 (2)} - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1.4.2

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

$8 \sqrt{2} + 5 \sqrt{4^{2} \cdot 2} - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1.5

Pull terms out from under the radical.

$8 \sqrt{2} + 5 (4 \sqrt{2}) - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1.6

Multiply $4$ by $5$ .

$8 \sqrt{2} + 20 \sqrt{2} - 7 \sqrt{128} + \sqrt{162} - \sqrt{722}$

Step 1.7

Rewrite $128$ as $8^{2} \cdot 2$ .

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Step 1.7.1

Factor $64$ out of $128$ .

$8 \sqrt{2} + 20 \sqrt{2} - 7 \sqrt{64 (2)} + \sqrt{162} - \sqrt{722}$

Step 1.7.2

Rewrite $64$ as $8^{2}$ .

$8 \sqrt{2} + 20 \sqrt{2} - 7 \sqrt{8^{2} \cdot 2} + \sqrt{162} - \sqrt{722}$

Step 1.8

Pull terms out from under the radical.

$8 \sqrt{2} + 20 \sqrt{2} - 7 (8 \sqrt{2}) + \sqrt{162} - \sqrt{722}$

Step 1.9

Multiply $8$ by $- 7$ .

$8 \sqrt{2} + 20 \sqrt{2} - 56 \sqrt{2} + \sqrt{162} - \sqrt{722}$

Step 1.10

Rewrite $162$ as $9^{2} \cdot 2$ .

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Step 1.10.1

Factor $81$ out of $162$ .

$8 \sqrt{2} + 20 \sqrt{2} - 56 \sqrt{2} + \sqrt{81 (2)} - \sqrt{722}$

Step 1.10.2

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

$8 \sqrt{2} + 20 \sqrt{2} - 56 \sqrt{2} + \sqrt{9^{2} \cdot 2} - \sqrt{722}$

Step 1.11

Pull terms out from under the radical.

$8 \sqrt{2} + 20 \sqrt{2} - 56 \sqrt{2} + 9 \sqrt{2} - \sqrt{722}$

Step 1.12

Rewrite $722$ as $19^{2} \cdot 2$ .

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Step 1.12.1

Factor $361$ out of $722$ .

$8 \sqrt{2} + 20 \sqrt{2} - 56 \sqrt{2} + 9 \sqrt{2} - \sqrt{361 (2)}$

Step 1.12.2

Rewrite $361$ as $19^{2}$ .

$8 \sqrt{2} + 20 \sqrt{2} - 56 \sqrt{2} + 9 \sqrt{2} - \sqrt{19^{2} \cdot 2}$

Step 1.13

Pull terms out from under the radical.

$8 \sqrt{2} + 20 \sqrt{2} - 56 \sqrt{2} + 9 \sqrt{2} - (19 \sqrt{2})$

Step 1.14

Multiply $19$ by $- 1$ .

$8 \sqrt{2} + 20 \sqrt{2} - 56 \sqrt{2} + 9 \sqrt{2} - 19 \sqrt{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $8 \sqrt{2}$ and $20 \sqrt{2}$ .

$28 \sqrt{2} - 56 \sqrt{2} + 9 \sqrt{2} - 19 \sqrt{2}$

Step 2.2

Subtract $56 \sqrt{2}$ from $28 \sqrt{2}$ .

$- 28 \sqrt{2} + 9 \sqrt{2} - 19 \sqrt{2}$

Step 2.3

Add $- 28 \sqrt{2}$ and $9 \sqrt{2}$ .

$- 19 \sqrt{2} - 19 \sqrt{2}$

Step 2.4

Subtract $19 \sqrt{2}$ from $- 19 \sqrt{2}$ .

$- 38 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 38 \sqrt{2}$

Decimal Form:

$- 53.74011537 \dots$