Simplify 4 square root of 216y^2+3 square root of 54y^2

$4 \sqrt{216 y^{2}} + 3 \sqrt{54 y^{2}}$

Step 1

Simplify each term.

Rewrite $216 y^{2}$ as ${(6 y)}^{2} \cdot 6$ .

Factor $36$ out of $216$ .

$4 \sqrt{36 (6) y^{2}} + 3 \sqrt{54 y^{2}}$

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

$4 \sqrt{6^{2} \cdot 6 y^{2}} + 3 \sqrt{54 y^{2}}$

Move $6$ .

$4 \sqrt{6^{2} y^{2} \cdot 6} + 3 \sqrt{54 y^{2}}$

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

$4 \sqrt{{(6 y)}^{2} \cdot 6} + 3 \sqrt{54 y^{2}}$

Pull terms out from under the radical.

$4 (6 y \sqrt{6}) + 3 \sqrt{54 y^{2}}$

Multiply $6$ by $4$ .

$24 (y \sqrt{6}) + 3 \sqrt{54 y^{2}}$

Rewrite $54 y^{2}$ as ${(3 y)}^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$24 y \sqrt{6} + 3 \sqrt{9 (6) y^{2}}$

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

$24 y \sqrt{6} + 3 \sqrt{3^{2} \cdot 6 y^{2}}$

Move $6$ .

$24 y \sqrt{6} + 3 \sqrt{3^{2} y^{2} \cdot 6}$

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

$24 y \sqrt{6} + 3 \sqrt{{(3 y)}^{2} \cdot 6}$

Pull terms out from under the radical.

$24 y \sqrt{6} + 3 (3 y \sqrt{6})$

Multiply $3$ by $3$ .

$24 y \sqrt{6} + 9 y \sqrt{6}$

Step 2

Add $24 y \sqrt{6}$ and $9 y \sqrt{6}$ .

$33 y \sqrt{6}$