Simplify square root of 5x- square root of 45x+ cube root of 81x- cube root of 24x

$\sqrt{5 x} - \sqrt{45 x} + \sqrt[3]{81 x} - \sqrt[3]{24 x}$

Simplify each term.

Rewrite $45 x$ as $3^{2} \cdot (5 x)$ .

Factor $9$ out of $45$ .

$\sqrt{5 x} - \sqrt{9 (5) x} + \sqrt[3]{81 x} - \sqrt[3]{24 x}$

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

$\sqrt{5 x} - \sqrt{3^{2} \cdot 5 x} + \sqrt[3]{81 x} - \sqrt[3]{24 x}$

Add parentheses.

$\sqrt{5 x} - \sqrt{3^{2} \cdot (5 x)} + \sqrt[3]{81 x} - \sqrt[3]{24 x}$

Pull terms out from under the radical.

$\sqrt{5 x} - (3 \sqrt{5 x}) + \sqrt[3]{81 x} - \sqrt[3]{24 x}$

Multiply $3$ by $- 1$ .

$\sqrt{5 x} - 3 \sqrt{5 x} + \sqrt[3]{81 x} - \sqrt[3]{24 x}$

Rewrite $81 x$ as $3^{3} \cdot (3 x)$ .

Factor $27$ out of $81$ .

$\sqrt{5 x} - 3 \sqrt{5 x} + \sqrt[3]{27 (3) x} - \sqrt[3]{24 x}$

Rewrite $27$ as $3^{3}$ .

$\sqrt{5 x} - 3 \sqrt{5 x} + \sqrt[3]{3^{3} \cdot 3 x} - \sqrt[3]{24 x}$

Add parentheses.

$\sqrt{5 x} - 3 \sqrt{5 x} + \sqrt[3]{3^{3} \cdot (3 x)} - \sqrt[3]{24 x}$

Pull terms out from under the radical.

$\sqrt{5 x} - 3 \sqrt{5 x} + 3 \sqrt[3]{3 x} - \sqrt[3]{24 x}$

Rewrite $24 x$ as $2^{3} \cdot (3 x)$ .

Factor $8$ out of $24$ .

$\sqrt{5 x} - 3 \sqrt{5 x} + 3 \sqrt[3]{3 x} - \sqrt[3]{8 (3) x}$

Rewrite $8$ as $2^{3}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

$\sqrt{5 x} - 3 \sqrt{5 x} + 3 \sqrt[3]{3 x} - 2 \sqrt[3]{3 x}$

Simplify by adding terms.

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

$- 2 \sqrt{5 x} + 3 \sqrt[3]{3 x} - 2 \sqrt[3]{3 x}$

Subtract $2 \sqrt[3]{3 x}$ from $3 \sqrt[3]{3 x}$ .

$- 2 \sqrt{5 x} + \sqrt[3]{3 x}$