Simplify square root of 8x^3+ square root of 2x^5-3 square root of 50x

$\sqrt{8 x^{3}} + \sqrt{2 x^{5}} - 3 \sqrt{50 x}$

Step 1

Rewrite $8 x^{3}$ as ${(2 x)}^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2) x^{3}} + \sqrt{2 x^{5}} - 3 \sqrt{50 x}$

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

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

Factor out $x^{2}$ .

$\sqrt{2^{2} \cdot 2 (x^{2} x)} + \sqrt{2 x^{5}} - 3 \sqrt{50 x}$

Move $2$ .

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

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

$\sqrt{{(2 x)}^{2} \cdot 2 x} + \sqrt{2 x^{5}} - 3 \sqrt{50 x}$

Add parentheses.

$\sqrt{{(2 x)}^{2} \cdot (2 x)} + \sqrt{2 x^{5}} - 3 \sqrt{50 x}$

Step 2

Pull terms out from under the radical.

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

Step 3

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

Factor out $x^{4}$ .

$2 x \sqrt{2 x} + \sqrt{2 (x^{4} x)} - 3 \sqrt{50 x}$

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

$2 x \sqrt{2 x} + \sqrt{2 ({(x^{2})}^{2} x)} - 3 \sqrt{50 x}$

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

$2 x \sqrt{2 x} + \sqrt{{(x^{2})}^{2} \cdot 2 x} - 3 \sqrt{50 x}$

Add parentheses.

$2 x \sqrt{2 x} + \sqrt{{(x^{2})}^{2} \cdot (2 x)} - 3 \sqrt{50 x}$

Step 4

Pull terms out from under the radical.

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

Step 5

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

Factor $25$ out of $50$ .

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

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

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

Add parentheses.

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $5$ by $- 3$ .

$2 x \sqrt{2 x} + x^{2} \sqrt{2 x} - 15 \sqrt{2 x}$