Simplify x square root of 72x^3-3 square root of 8x^5+x square root of 2x^3

$x \sqrt{72 x^{3}} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Step 1

Simplify each term.

Rewrite $72 x^{3}$ as ${(6 x)}^{2} \cdot (2 x)$ .

Factor $36$ out of $72$ .

$x \sqrt{36 (2) x^{3}} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Rewrite $36$ as $6^{2}$ .

$x \sqrt{6^{2} \cdot 2 x^{3}} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Factor out $x^{2}$ .

$x \sqrt{6^{2} \cdot 2 (x^{2} x)} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Move $2$ .

$x \sqrt{6^{2} x^{2} \cdot 2 x} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

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

$x \sqrt{{(6 x)}^{2} \cdot 2 x} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Add parentheses.

$x \sqrt{{(6 x)}^{2} \cdot (2 x)} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Pull terms out from under the radical.

$x (6 x \sqrt{2 x}) - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Rewrite using the commutative property of multiplication.

$6 x (x \sqrt{2 x}) - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$6 (x \cdot x) \sqrt{2 x} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Multiply $x$ by $x$ .

$6 x^{2} \sqrt{2 x} - 3 \sqrt{8 x^{5}} + x \sqrt{2 x^{3}}$

Rewrite $8 x^{5}$ as ${(2 x^{2})}^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

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

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

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

Factor out $x^{4}$ .

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

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 3$ .

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

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

Factor out $x^{2}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Step 2

Simplify by adding terms.

Subtract $6 x^{2} \sqrt{2 x}$ from $6 x^{2} \sqrt{2 x}$ .

$0 + x^{2} \sqrt{2 x}$

Add $0$ and $x^{2} \sqrt{2 x}$ .

$x^{2} \sqrt{2 x}$

Simplify x square root of 72x^3-3 square root of 8x^5+x square root of 2x^3

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