Evaluate square root of 75- square root of 48

$\sqrt{75} - \sqrt{48}$

Step 1

Simplify each term.

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

Factor $25$ out of $75$ .

$\sqrt{25 (3)} - \sqrt{48}$

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

$\sqrt{5^{2} \cdot 3} - \sqrt{48}$

$\sqrt{5^{2} \cdot 3} - \sqrt{48}$

Pull terms out from under the radical.

$5 \sqrt{3} - \sqrt{48}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$5 \sqrt{3} - \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$5 \sqrt{3} - \sqrt{4^{2} \cdot 3}$

$5 \sqrt{3} - \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$5 \sqrt{3} - (4 \sqrt{3})$

Multiply $4$ by $- 1$ .

$5 \sqrt{3} - 4 \sqrt{3}$

$5 \sqrt{3} - 4 \sqrt{3}$

Step 2

Subtract $4 \sqrt{3}$ from $5 \sqrt{3}$ .

$\sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$

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