Simplify 8x square root of 96-10 square root of 54x^2

$8 x \sqrt{96} - 10 \sqrt{54 x^{2}}$

Step 1

Simplify each term.

Rewrite $96$ as $4^{2} \cdot 6$ .

Factor $16$ out of $96$ .

$8 x \sqrt{16 (6)} - 10 \sqrt{54 x^{2}}$

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

$8 x \sqrt{4^{2} \cdot 6} - 10 \sqrt{54 x^{2}}$

$8 x \sqrt{4^{2} \cdot 6} - 10 \sqrt{54 x^{2}}$

Pull terms out from under the radical.

$8 x (4 \sqrt{6}) - 10 \sqrt{54 x^{2}}$

Multiply $4$ by $8$ .

$32 x \sqrt{6} - 10 \sqrt{54 x^{2}}$

Rewrite $54 x^{2}$ as ${(3 x)}^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$32 x \sqrt{6} - 10 \sqrt{9 (6) x^{2}}$

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

$32 x \sqrt{6} - 10 \sqrt{3^{2} \cdot 6 x^{2}}$

Move $6$ .

$32 x \sqrt{6} - 10 \sqrt{3^{2} x^{2} \cdot 6}$

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

$32 x \sqrt{6} - 10 \sqrt{{(3 x)}^{2} \cdot 6}$

$32 x \sqrt{6} - 10 \sqrt{{(3 x)}^{2} \cdot 6}$

Pull terms out from under the radical.

$32 x \sqrt{6} - 10 (3 x \sqrt{6})$

Multiply $3$ by $- 10$ .

$32 x \sqrt{6} - 30 x \sqrt{6}$

$32 x \sqrt{6} - 30 x \sqrt{6}$

Step 2

Subtract $30 x \sqrt{6}$ from $32 x \sqrt{6}$ .

$2 x \sqrt{6}$

Related Questions