Evaluate square root of 27+ square root of 75

$\sqrt{27} + \sqrt{75}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$\sqrt{9 (3)} + \sqrt{75}$

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

$\sqrt{3^{2} \cdot 3} + \sqrt{75}$

$\sqrt{3^{2} \cdot 3} + \sqrt{75}$

Pull terms out from under the radical.

$3 \sqrt{3} + \sqrt{75}$

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

Factor $25$ out of $75$ .

$3 \sqrt{3} + \sqrt{25 (3)}$

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

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

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

Pull terms out from under the radical.

$3 \sqrt{3} + 5 \sqrt{3}$

$3 \sqrt{3} + 5 \sqrt{3}$

Step 2

Add $3 \sqrt{3}$ and $5 \sqrt{3}$ .

$8 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{3}$

Decimal Form:

$13.85640646 \dots$

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