Simplify 8 square root of 72- square root of 162+4 square root of 50

$8 \sqrt{72} - \sqrt{162} + 4 \sqrt{50}$

Simplify each term.

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Rewrite $72$ as $6^{2} \cdot 2$ .

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Factor $36$ out of $72$ .

$8 \sqrt{36 (2)} - \sqrt{162} + 4 \sqrt{50}$

Rewrite $36$ as $6^{2}$ .

$8 \sqrt{6^{2} \cdot 2} - \sqrt{162} + 4 \sqrt{50}$

Pull terms out from under the radical.

$8 (6 \sqrt{2}) - \sqrt{162} + 4 \sqrt{50}$

Multiply $6$ by $8$ .

$48 \sqrt{2} - \sqrt{162} + 4 \sqrt{50}$

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

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Factor $81$ out of $162$ .

$48 \sqrt{2} - \sqrt{81 (2)} + 4 \sqrt{50}$

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

$48 \sqrt{2} - \sqrt{9^{2} \cdot 2} + 4 \sqrt{50}$

Pull terms out from under the radical.

$48 \sqrt{2} - (9 \sqrt{2}) + 4 \sqrt{50}$

Multiply $9$ by $- 1$ .

$48 \sqrt{2} - 9 \sqrt{2} + 4 \sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

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Factor $25$ out of $50$ .

$48 \sqrt{2} - 9 \sqrt{2} + 4 \sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

$48 \sqrt{2} - 9 \sqrt{2} + 4 \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$48 \sqrt{2} - 9 \sqrt{2} + 4 (5 \sqrt{2})$

Multiply $5$ by $4$ .

$48 \sqrt{2} - 9 \sqrt{2} + 20 \sqrt{2}$

Simplify by adding terms.

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Subtract $9 \sqrt{2}$ from $48 \sqrt{2}$ .

$39 \sqrt{2} + 20 \sqrt{2}$

Add $39 \sqrt{2}$ and $20 \sqrt{2}$ .

$59 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$59 \sqrt{2}$

Decimal Form:

$83.43860018 \dots$

Simplify 8 square root of 72- square root of 162+4 square root of 50