Evaluate square root of 18- square root of 72

$\sqrt{18} - \sqrt{72}$

Step 1

Simplify each term.

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

Factor $9$ out of $18$ .

$\sqrt{9 (2)} - \sqrt{72}$

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

$\sqrt{3^{2} \cdot 2} - \sqrt{72}$

$\sqrt{3^{2} \cdot 2} - \sqrt{72}$

Pull terms out from under the radical.

$3 \sqrt{2} - \sqrt{72}$

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

Factor $36$ out of $72$ .

$3 \sqrt{2} - \sqrt{36 (2)}$

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

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

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

Pull terms out from under the radical.

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

Multiply $6$ by $- 1$ .

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

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

Step 2

Subtract $6 \sqrt{2}$ from $3 \sqrt{2}$ .

$- 3 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{2}$

Decimal Form:

$- 4.24264068 \dots$

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