Evaluate square root of 108- square root of 75

$\sqrt{108} - \sqrt{75}$

Step 1

Simplify each term.

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$\sqrt{36 (3)} - \sqrt{75}$

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

$\sqrt{6^{2} \cdot 3} - \sqrt{75}$

$\sqrt{6^{2} \cdot 3} - \sqrt{75}$

Pull terms out from under the radical.

$6 \sqrt{3} - \sqrt{75}$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $- 1$ .

$6 \sqrt{3} - 5 \sqrt{3}$

$6 \sqrt{3} - 5 \sqrt{3}$

Step 2

Subtract $5 \sqrt{3}$ from $6 \sqrt{3}$ .

$\sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$

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