Simplify - square root of 147+ square root of 192- square root of 243

$- \sqrt{147} + \sqrt{192} - \sqrt{243}$

Step 1

Simplify each term.

Rewrite $147$ as $7^{2} \cdot 3$ .

Factor $49$ out of $147$ .

$- \sqrt{49 (3)} + \sqrt{192} - \sqrt{243}$

Rewrite $49$ as $7^{2}$ .

$- \sqrt{7^{2} \cdot 3} + \sqrt{192} - \sqrt{243}$

Pull terms out from under the radical.

$- (7 \sqrt{3}) + \sqrt{192} - \sqrt{243}$

Multiply $7$ by $- 1$ .

$- 7 \sqrt{3} + \sqrt{192} - \sqrt{243}$

Rewrite $192$ as $8^{2} \cdot 3$ .

Factor $64$ out of $192$ .

$- 7 \sqrt{3} + \sqrt{64 (3)} - \sqrt{243}$

Rewrite $64$ as $8^{2}$ .

$- 7 \sqrt{3} + \sqrt{8^{2} \cdot 3} - \sqrt{243}$

Pull terms out from under the radical.

$- 7 \sqrt{3} + 8 \sqrt{3} - \sqrt{243}$

Rewrite $243$ as $9^{2} \cdot 3$ .

Factor $81$ out of $243$ .

$- 7 \sqrt{3} + 8 \sqrt{3} - \sqrt{81 (3)}$

Rewrite $81$ as $9^{2}$ .

$- 7 \sqrt{3} + 8 \sqrt{3} - \sqrt{9^{2} \cdot 3}$

Pull terms out from under the radical.

$- 7 \sqrt{3} + 8 \sqrt{3} - (9 \sqrt{3})$

Multiply $9$ by $- 1$ .

$- 7 \sqrt{3} + 8 \sqrt{3} - 9 \sqrt{3}$

Step 2

Simplify by adding terms.

Add $- 7 \sqrt{3}$ and $8 \sqrt{3}$ .

$\sqrt{3} - 9 \sqrt{3}$

Subtract $9 \sqrt{3}$ from $\sqrt{3}$ .

$- 8 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 8 \sqrt{3}$

Decimal Form:

$- 13.85640646 \dots$