Simplify the Radical Expression 7 square root of 4(5 square root of 3-2 square root of 3)

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

Step 1

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

Multiply $7$ by $2$ .

$14 (5 \sqrt{3} - 2 \sqrt{3})$

Step 5

Subtract $2 \sqrt{3}$ from $5 \sqrt{3}$ .

$14 (3 \sqrt{3})$

Step 6

Multiply $3$ by $14$ .

$42 \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$42 \sqrt{3}$

Decimal Form:

$72.74613391 \dots$