Simplify square root of 6x^7-x square root of 96x^5

$\sqrt{6 x^{7}} - x \sqrt{96 x^{5}}$

Step 1

Simplify each term.

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

Factor out $x^{6}$ .

$\sqrt{6 (x^{6} x)} - x \sqrt{96 x^{5}}$

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

$\sqrt{6 ({(x^{3})}^{2} x)} - x \sqrt{96 x^{5}}$

Reorder $6$ and ${(x^{3})}^{2}$ .

$\sqrt{{(x^{3})}^{2} \cdot 6 x} - x \sqrt{96 x^{5}}$

Add parentheses.

$\sqrt{{(x^{3})}^{2} \cdot (6 x)} - x \sqrt{96 x^{5}}$

Pull terms out from under the radical.

$x^{3} \sqrt{6 x} - x \sqrt{96 x^{5}}$

Rewrite $96 x^{5}$ as ${(4 x^{2})}^{2} \cdot (6 x)$ .

Factor $16$ out of $96$ .

$x^{3} \sqrt{6 x} - x \sqrt{16 (6) x^{5}}$

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

$x^{3} \sqrt{6 x} - x \sqrt{4^{2} \cdot 6 x^{5}}$

Factor out $x^{4}$ .

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

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

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

Move $6$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

Move $x^{2}$ .

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

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

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

$x^{3} \sqrt{6 x} - (x^{2} x^{1}) (4 \sqrt{6 x})$

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

$x^{3} \sqrt{6 x} - x^{2 + 1} (4 \sqrt{6 x})$

Add $2$ and $1$ .

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

Multiply $4$ by $- 1$ .

$x^{3} \sqrt{6 x} - 4 x^{3} \sqrt{6 x}$

Step 2

Subtract $4 x^{3} \sqrt{6 x}$ from $x^{3} \sqrt{6 x}$ .

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

Simplify square root of 6x^7-x square root of 96x^5

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