Simplify square root of 12+5 square root of 8-7 square root of 20

$\sqrt{12} + 5 \sqrt{8} - 7 \sqrt{20}$

Step 1

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3)} + 5 \sqrt{8} - 7 \sqrt{20}$

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

$\sqrt{2^{2} \cdot 3} + 5 \sqrt{8} - 7 \sqrt{20}$

Step 2

Pull terms out from under the radical.

$2 \sqrt{3} + 5 \sqrt{8} - 7 \sqrt{20}$

Step 3

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

Factor $4$ out of $8$ .

$2 \sqrt{3} + 5 \sqrt{4 (2)} - 7 \sqrt{20}$

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

$2 \sqrt{3} + 5 \sqrt{2^{2} \cdot 2} - 7 \sqrt{20}$

Step 4

Pull terms out from under the radical.

$2 \sqrt{3} + 5 (2 \sqrt{2}) - 7 \sqrt{20}$

Step 5

Multiply $2$ by $5$ .

$2 \sqrt{3} + 10 \sqrt{2} - 7 \sqrt{20}$

Step 6

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$2 \sqrt{3} + 10 \sqrt{2} - 7 \sqrt{4 (5)}$

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

$2 \sqrt{3} + 10 \sqrt{2} - 7 \sqrt{2^{2} \cdot 5}$

Step 7

Pull terms out from under the radical.

$2 \sqrt{3} + 10 \sqrt{2} - 7 (2 \sqrt{5})$

Step 8

Multiply $2$ by $- 7$ .

$2 \sqrt{3} + 10 \sqrt{2} - 14 \sqrt{5}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3} + 10 \sqrt{2} - 14 \sqrt{5}$

Decimal Form:

$- 13.69871444 \dots$