Simplify -x^2 square root of 24x^2+7x square root of 6x^4

$- x^{2} \sqrt{24 x^{2}} + 7 x \sqrt{6 x^{4}}$

Step 1

Simplify each term.

Rewrite $24 x^{2}$ as ${(2 x)}^{2} \cdot 6$ .

Factor $4$ out of $24$ .

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

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

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

Move $6$ .

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

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

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

Pull terms out from under the radical.

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

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

Move $x$ .

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

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

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

$- (x^{1} x^{2}) (2 \sqrt{6}) + 7 x \sqrt{6 x^{4}}$

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

$- x^{1 + 2} (2 \sqrt{6}) + 7 x \sqrt{6 x^{4}}$

Add $1$ and $2$ .

$- x^{3} (2 \sqrt{6}) + 7 x \sqrt{6 x^{4}}$

Multiply $2$ by $- 1$ .

$- 2 x^{3} \sqrt{6} + 7 x \sqrt{6 x^{4}}$

Rewrite $6 x^{4}$ as ${(x^{2})}^{2} \cdot 6$ .

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

$- 2 x^{3} \sqrt{6} + 7 x \sqrt{6 {(x^{2})}^{2}}$

Reorder $6$ and ${(x^{2})}^{2}$ .

$- 2 x^{3} \sqrt{6} + 7 x \sqrt{{(x^{2})}^{2} \cdot 6}$

Pull terms out from under the radical.

$- 2 x^{3} \sqrt{6} + 7 x (x^{2} \sqrt{6})$

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

Move $x^{2}$ .

$- 2 x^{3} \sqrt{6} + 7 (x^{2} x) \sqrt{6}$

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

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

$- 2 x^{3} \sqrt{6} + 7 (x^{2} x^{1}) \sqrt{6}$

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

$- 2 x^{3} \sqrt{6} + 7 x^{2 + 1} \sqrt{6}$

Add $2$ and $1$ .

$- 2 x^{3} \sqrt{6} + 7 x^{3} \sqrt{6}$

Step 2

Add $- 2 x^{3} \sqrt{6}$ and $7 x^{3} \sqrt{6}$ .

$5 x^{3} \sqrt{6}$

Simplify -x^2 square root of 24x^2+7x square root of 6x^4

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