Evaluate 3 square root of 27-2 square root of 18+ square root of 48

$3 \sqrt{27} - 2 \sqrt{18} + \sqrt{48}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$3 \sqrt{9 (3)} - 2 \sqrt{18} + \sqrt{48}$

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

$3 \sqrt{3^{2} \cdot 3} - 2 \sqrt{18} + \sqrt{48}$

$3 \sqrt{3^{2} \cdot 3} - 2 \sqrt{18} + \sqrt{48}$

Pull terms out from under the radical.

$3 (3 \sqrt{3}) - 2 \sqrt{18} + \sqrt{48}$

Multiply $3$ by $3$ .

$9 \sqrt{3} - 2 \sqrt{18} + \sqrt{48}$

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

Factor $9$ out of $18$ .

$9 \sqrt{3} - 2 \sqrt{9 (2)} + \sqrt{48}$

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

$9 \sqrt{3} - 2 \sqrt{3^{2} \cdot 2} + \sqrt{48}$

$9 \sqrt{3} - 2 \sqrt{3^{2} \cdot 2} + \sqrt{48}$

Pull terms out from under the radical.

$9 \sqrt{3} - 2 (3 \sqrt{2}) + \sqrt{48}$

Multiply $3$ by $- 2$ .

$9 \sqrt{3} - 6 \sqrt{2} + \sqrt{48}$

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

Factor $16$ out of $48$ .

$9 \sqrt{3} - 6 \sqrt{2} + \sqrt{16 (3)}$

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

$9 \sqrt{3} - 6 \sqrt{2} + \sqrt{4^{2} \cdot 3}$

$9 \sqrt{3} - 6 \sqrt{2} + \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$9 \sqrt{3} - 6 \sqrt{2} + 4 \sqrt{3}$

$9 \sqrt{3} - 6 \sqrt{2} + 4 \sqrt{3}$

Step 2

Add $9 \sqrt{3}$ and $4 \sqrt{3}$ .

$13 \sqrt{3} - 6 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{3} - 6 \sqrt{2}$

Decimal Form:

$14.03137912 \dots$

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