Simplify square root of 36x^3+ square root of 64x^3-x square root of 9xy

$\sqrt{36 x^{3}} + \sqrt{64 x^{3}} - x \sqrt{9 x y}$

Step 1

Simplify each term.

Rewrite $36 x^{3}$ as ${(6 x)}^{2} x$ .

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

$\sqrt{6^{2} x^{3}} + \sqrt{64 x^{3}} - x \sqrt{9 x y}$

Factor out $x^{2}$ .

$\sqrt{6^{2} (x^{2} x)} + \sqrt{64 x^{3}} - x \sqrt{9 x y}$

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

$\sqrt{{(6 x)}^{2} x} + \sqrt{64 x^{3}} - x \sqrt{9 x y}$

Pull terms out from under the radical.

$6 x \sqrt{x} + \sqrt{64 x^{3}} - x \sqrt{9 x y}$

Rewrite $64 x^{3}$ as ${(8 x)}^{2} x$ .

Rewrite $64$ as $8^{2}$ .

$6 x \sqrt{x} + \sqrt{8^{2} x^{3}} - x \sqrt{9 x y}$

Factor out $x^{2}$ .

$6 x \sqrt{x} + \sqrt{8^{2} (x^{2} x)} - x \sqrt{9 x y}$

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

$6 x \sqrt{x} + \sqrt{{(8 x)}^{2} x} - x \sqrt{9 x y}$

Pull terms out from under the radical.

$6 x \sqrt{x} + 8 x \sqrt{x} - x \sqrt{9 x y}$

Rewrite $9 x y$ as $3^{2} (x y)$ .

Rewrite $9$ as $3^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

$6 x \sqrt{x} + 8 x \sqrt{x} - x (3 \sqrt{x y})$

Multiply $3$ by $- 1$ .

$6 x \sqrt{x} + 8 x \sqrt{x} - 3 x \sqrt{x y}$

Step 2

Add $6 x \sqrt{x}$ and $8 x \sqrt{x}$ .

$14 x \sqrt{x} - 3 x \sqrt{x y}$