Evaluate square root of 18- square root of 50

$\sqrt{18} - \sqrt{50}$

Step 1

Simplify each term.

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

Factor $9$ out of $18$ .

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

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

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

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

Pull terms out from under the radical.

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

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

Factor $25$ out of $50$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $- 1$ .

$3 \sqrt{2} - 5 \sqrt{2}$

$3 \sqrt{2} - 5 \sqrt{2}$

Step 2

Subtract $5 \sqrt{2}$ from $3 \sqrt{2}$ .

$- 2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{2}$

Decimal Form:

$- 2.82842712 \dots$

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