Simplify - square root of 7x^6-x^2 square root of 7x^2

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

Step 1

Simplify each term.

Rewrite $7 x^{6}$ as ${(x^{3})}^{2} \cdot 7$ .

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

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

Reorder $7$ and ${(x^{3})}^{2}$ .

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

Pull terms out from under the radical.

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

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

$- x^{3} \sqrt{7} - x^{2} \sqrt{x^{2} \cdot 7}$

Pull terms out from under the radical.

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$- x^{3} \sqrt{7} - (x^{1} x^{2}) \sqrt{7}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- x^{3} \sqrt{7} - x^{1 + 2} \sqrt{7}$

Add $1$ and $2$ .

$- x^{3} \sqrt{7} - x^{3} \sqrt{7}$

Step 2

Subtract $x^{3} \sqrt{7}$ from $- x^{3} \sqrt{7}$ .

$- 2 x^{3} \sqrt{7}$