Evaluate 4 square root of 63-9 square root of 28+2 square root of 44

$4 \sqrt{63} - 9 \sqrt{28} + 2 \sqrt{44}$

Step 1

Simplify each term.

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$4 \sqrt{9 (7)} - 9 \sqrt{28} + 2 \sqrt{44}$

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

$4 \sqrt{3^{2} \cdot 7} - 9 \sqrt{28} + 2 \sqrt{44}$

Pull terms out from under the radical.

$4 (3 \sqrt{7}) - 9 \sqrt{28} + 2 \sqrt{44}$

Multiply $3$ by $4$ .

$12 \sqrt{7} - 9 \sqrt{28} + 2 \sqrt{44}$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$12 \sqrt{7} - 9 \sqrt{4 (7)} + 2 \sqrt{44}$

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

$12 \sqrt{7} - 9 \sqrt{2^{2} \cdot 7} + 2 \sqrt{44}$

Pull terms out from under the radical.

$12 \sqrt{7} - 9 (2 \sqrt{7}) + 2 \sqrt{44}$

Multiply $2$ by $- 9$ .

$12 \sqrt{7} - 18 \sqrt{7} + 2 \sqrt{44}$

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$12 \sqrt{7} - 18 \sqrt{7} + 2 \sqrt{4 (11)}$

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

$12 \sqrt{7} - 18 \sqrt{7} + 2 \sqrt{2^{2} \cdot 11}$

Pull terms out from under the radical.

$12 \sqrt{7} - 18 \sqrt{7} + 2 (2 \sqrt{11})$

Multiply $2$ by $2$ .

$12 \sqrt{7} - 18 \sqrt{7} + 4 \sqrt{11}$

Step 2

Subtract $18 \sqrt{7}$ from $12 \sqrt{7}$ .

$- 6 \sqrt{7} + 4 \sqrt{11}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 6 \sqrt{7} + 4 \sqrt{11}$

Decimal Form:

$- 2.60800870 \dots$