Simplify the Radical Expression 6x square root of 112-6 square root of 7x^2

$6 x \sqrt{112} - 6 \sqrt{7 x^{2}}$

Step 1

Rewrite $112$ as $4^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$6 x \sqrt{16 (7)} - 6 \sqrt{7 x^{2}}$

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

$6 x \sqrt{4^{2} \cdot 7} - 6 \sqrt{7 x^{2}}$

Step 2

Pull terms out from under the radical.

$6 x (| 4 | \sqrt{7}) - 6 \sqrt{7 x^{2}}$

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$6 x (4 \sqrt{7}) - 6 \sqrt{7 x^{2}}$

Step 4

Multiply $4$ by $6$ .

$24 x \sqrt{7} - 6 \sqrt{7 x^{2}}$

Step 5

Reorder $7$ and $x^{2}$ .

$24 x \sqrt{7} - 6 \sqrt{x^{2} \cdot 7}$

Step 6

Pull terms out from under the radical.

$24 x \sqrt{7} - 6 | x | \sqrt{7}$