Algebra Examples

$\sqrt{x^{3}} + \sqrt{16 x^{3}} - 3 x \sqrt{x}$

Step 1

Simplify each term.

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Step 1.1

Factor out $x^{2}$ .

$\sqrt{x^{2} x} + \sqrt{16 x^{3}} - 3 x \sqrt{x}$

Step 1.2

Pull terms out from under the radical.

$x \sqrt{x} + \sqrt{16 x^{3}} - 3 x \sqrt{x}$

Step 1.3

Rewrite $16 x^{3}$ as ${(4 x)}^{2} x$ .

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Step 1.3.1

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

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

Step 1.3.2

Factor out $x^{2}$ .

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

Step 1.3.3

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 2

Simplify by adding terms.

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Step 2.1

Add $x \sqrt{x}$ and $4 x \sqrt{x}$ .

$5 x \sqrt{x} - 3 x \sqrt{x}$

Step 2.2

Subtract $3 x \sqrt{x}$ from $5 x \sqrt{x}$ .

$2 x \sqrt{x}$