Simplify square root of 50x^3- square root of 25x^3+5 square root of x^3- square root of 2x^3

$\sqrt{50 x^{3}} - \sqrt{25 x^{3}} + 5 \sqrt{x^{3}} - \sqrt{2 x^{3}}$

Step 1

Simplify each term.

Rewrite $50 x^{3}$ as ${(5 x)}^{2} \cdot (2 x)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) x^{3}} - \sqrt{25 x^{3}} + 5 \sqrt{x^{3}} - \sqrt{2 x^{3}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2 x^{3}} - \sqrt{25 x^{3}} + 5 \sqrt{x^{3}} - \sqrt{2 x^{3}}$

Factor out $x^{2}$ .

$\sqrt{5^{2} \cdot 2 (x^{2} x)} - \sqrt{25 x^{3}} + 5 \sqrt{x^{3}} - \sqrt{2 x^{3}}$

Move $2$ .

$\sqrt{5^{2} x^{2} \cdot 2 x} - \sqrt{25 x^{3}} + 5 \sqrt{x^{3}} - \sqrt{2 x^{3}}$

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

$\sqrt{{(5 x)}^{2} \cdot 2 x} - \sqrt{25 x^{3}} + 5 \sqrt{x^{3}} - \sqrt{2 x^{3}}$

Add parentheses.

$\sqrt{{(5 x)}^{2} \cdot (2 x)} - \sqrt{25 x^{3}} + 5 \sqrt{x^{3}} - \sqrt{2 x^{3}}$

Pull terms out from under the radical.

$5 x \sqrt{2 x} - \sqrt{25 x^{3}} + 5 \sqrt{x^{3}} - \sqrt{2 x^{3}}$

Rewrite $25 x^{3}$ as ${(5 x)}^{2} x$ .

Rewrite $25$ as $5^{2}$ .

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

Factor out $x^{2}$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $- 1$ .

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

Factor out $x^{2}$ .

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

Pull terms out from under the radical.

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

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

Factor out $x^{2}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$5 x \sqrt{2 x} - 5 x \sqrt{x} + 5 x \sqrt{x} - x \sqrt{2 x}$

Step 2

Simplify by adding terms.

Combine the opposite terms in $5 x \sqrt{2 x} - 5 x \sqrt{x} + 5 x \sqrt{x} - x \sqrt{2 x}$ .

Add $- 5 x \sqrt{x}$ and $5 x \sqrt{x}$ .

$5 x \sqrt{2 x} + 0 - x \sqrt{2 x}$

Add $5 x \sqrt{2 x}$ and $0$ .

$5 x \sqrt{2 x} - x \sqrt{2 x}$

Subtract $x \sqrt{2 x}$ from $5 x \sqrt{2 x}$ .

$4 x \sqrt{2 x}$

Simplify square root of 50x^3- square root of 25x^3+5 square root of x^3- square root of 2x^3

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