Evaluate square root of 18- square root of 54+2 square root of 50

$\sqrt{18} - \sqrt{54} + 2 \sqrt{50}$

Simplify each term.

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Rewrite $18$ as $3^{2} \cdot 2$ .

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Factor $9$ out of $18$ .

$\sqrt{9 (2)} - \sqrt{54} + 2 \sqrt{50}$

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

$\sqrt{3^{2} \cdot 2} - \sqrt{54} + 2 \sqrt{50}$

Pull terms out from under the radical.

$3 \sqrt{2} - \sqrt{54} + 2 \sqrt{50}$

Rewrite $54$ as $3^{2} \cdot 6$ .

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Factor $9$ out of $54$ .

$3 \sqrt{2} - \sqrt{9 (6)} + 2 \sqrt{50}$

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

$3 \sqrt{2} - \sqrt{3^{2} \cdot 6} + 2 \sqrt{50}$

Pull terms out from under the radical.

$3 \sqrt{2} - (3 \sqrt{6}) + 2 \sqrt{50}$

Multiply $3$ by $- 1$ .

$3 \sqrt{2} - 3 \sqrt{6} + 2 \sqrt{50}$

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

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Factor $25$ out of $50$ .

$3 \sqrt{2} - 3 \sqrt{6} + 2 \sqrt{25 (2)}$

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

$3 \sqrt{2} - 3 \sqrt{6} + 2 \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$3 \sqrt{2} - 3 \sqrt{6} + 2 (5 \sqrt{2})$

Multiply $5$ by $2$ .

$3 \sqrt{2} - 3 \sqrt{6} + 10 \sqrt{2}$

Add $3 \sqrt{2}$ and $10 \sqrt{2}$ .

$13 \sqrt{2} - 3 \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{2} - 3 \sqrt{6}$

Decimal Form:

$11.03630708 \dots$

Evaluate square root of 18- square root of 54+2 square root of 50

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