Simplify -x^3 square root of 3+x square root of 147x^4

$- x^{3} \sqrt{3} + x \sqrt{147 x^{4}}$

Simplify each term.

Rewrite $147 x^{4}$ as ${(7 x^{2})}^{2} \cdot 3$ .

Factor $49$ out of $147$ .

$- x^{3} \sqrt{3} + x \sqrt{49 (3) x^{4}}$

Rewrite $49$ as $7^{2}$ .

$- x^{3} \sqrt{3} + x \sqrt{7^{2} \cdot 3 x^{4}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Move $3$ .

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

Rewrite $7^{2} {(x^{2})}^{2}$ as ${(7 x^{2})}^{2}$ .

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Simplify by adding terms.

Reorder the factors of $7 \sqrt{3} x^{3}$ .

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

Add $- x^{3} \sqrt{3}$ and $7 x^{3} \sqrt{3}$ .

$6 x^{3} \sqrt{3}$