Simplify 3 square root of 20x+8 square root of 45x-4 square root of 5x

$3 \sqrt{20 x} + 8 \sqrt{45 x} - 4 \sqrt{5 x}$

Step 1

Simplify each term.

Rewrite $20 x$ as $2^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$3 \sqrt{4 (5) x} + 8 \sqrt{45 x} - 4 \sqrt{5 x}$

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

$3 \sqrt{2^{2} \cdot 5 x} + 8 \sqrt{45 x} - 4 \sqrt{5 x}$

Add parentheses.

$3 \sqrt{2^{2} \cdot (5 x)} + 8 \sqrt{45 x} - 4 \sqrt{5 x}$

Pull terms out from under the radical.

$3 (2 \sqrt{5 x}) + 8 \sqrt{45 x} - 4 \sqrt{5 x}$

Multiply $2$ by $3$ .

$6 \sqrt{5 x} + 8 \sqrt{45 x} - 4 \sqrt{5 x}$

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

Factor $9$ out of $45$ .

$6 \sqrt{5 x} + 8 \sqrt{9 (5) x} - 4 \sqrt{5 x}$

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

$6 \sqrt{5 x} + 8 \sqrt{3^{2} \cdot 5 x} - 4 \sqrt{5 x}$

Add parentheses.

$6 \sqrt{5 x} + 8 \sqrt{3^{2} \cdot (5 x)} - 4 \sqrt{5 x}$

Pull terms out from under the radical.

$6 \sqrt{5 x} + 8 (3 \sqrt{5 x}) - 4 \sqrt{5 x}$

Multiply $3$ by $8$ .

$6 \sqrt{5 x} + 24 \sqrt{5 x} - 4 \sqrt{5 x}$

Step 2

Simplify by adding terms.

Add $6 \sqrt{5 x}$ and $24 \sqrt{5 x}$ .

$30 \sqrt{5 x} - 4 \sqrt{5 x}$

Subtract $4 \sqrt{5 x}$ from $30 \sqrt{5 x}$ .

$26 \sqrt{5 x}$