Simplify the Radical Expression 6x square root of 28x^5-x^2 square root of 7x^3

$6 x \sqrt{28 x^{5}} - x^{2} \sqrt{7 x^{3}}$

Step 1

Simplify each term.

Rewrite $28 x^{5}$ as ${(2 x^{2})}^{2} \cdot (7 x)$ .

Factor $4$ out of $28$ .

$6 x \sqrt{4 (7) x^{5}} - x^{2} \sqrt{7 x^{3}}$

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

$6 x \sqrt{2^{2} \cdot 7 x^{5}} - x^{2} \sqrt{7 x^{3}}$

Factor out $x^{4}$ .

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

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

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

Move $7$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $6$ .

$12 x^{3} \sqrt{7 x} - x^{2} \sqrt{7 x^{3}}$

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

Factor out $x^{2}$ .

$12 x^{3} \sqrt{7 x} - x^{2} \sqrt{7 (x^{2} x)}$

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

$12 x^{3} \sqrt{7 x} - x^{2} \sqrt{x^{2} \cdot 7 x}$

Add parentheses.

$12 x^{3} \sqrt{7 x} - x^{2} \sqrt{x^{2} \cdot (7 x)}$

Pull terms out from under the radical.

$12 x^{3} \sqrt{7 x} - x^{2} (| x | \sqrt{7 x})$

Step 2

Reorder factors in $12 x^{3} \sqrt{7 x} - x^{2} (| x | \sqrt{7 x})$ .

$12 x^{3} \sqrt{7 x} - x^{2} | x | \sqrt{7 x}$

Simplify the Radical Expression 6x square root of 28x^5-x^2 square root of 7x^3

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