Simplify the Radical Expression square root of 12-5 cube root of 8-7 square root of 20

$\sqrt{12} - 5 \sqrt[3]{8} - 7 \sqrt{20}$

Step 1

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

Factor $4$ out of $12$ .

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

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

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

Step 2

Pull terms out from under the radical.

$| 2 | \sqrt{3} - 5 \sqrt[3]{8} - 7 \sqrt{20}$

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 4

Rewrite $8$ as $2^{3}$ .

$2 \sqrt{3} - 5 \sqrt[3]{2^{3}} - 7 \sqrt{20}$

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $- 5$ by $2$ .

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

Step 7

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

Factor $4$ out of $20$ .

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

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 10

Multiply $2$ by $- 7$ .

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

Step 11

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 37.84085006 \dots$