Simplify square root of 75- square root of 27

$\sqrt{75} - \sqrt{27}$

Step 1

Simplify each term.

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

Factor $25$ out of $75$ .

$\sqrt{25 (3)} - \sqrt{27}$

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

$\sqrt{5^{2} \cdot 3} - \sqrt{27}$

$\sqrt{5^{2} \cdot 3} - \sqrt{27}$

Pull terms out from under the radical.

$5 \sqrt{3} - \sqrt{27}$

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$5 \sqrt{3} - \sqrt{9 (3)}$

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 1$ .

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

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

Step 2

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

$2 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3}$

Decimal Form:

$3.46410161 \dots$

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