Simplify square root of 27x^3y+x square root of 48xy

$\sqrt{27 x^{3} y} + x \sqrt{48 x y}$

Simplify each term.

Rewrite $27 x^{3} y$ as ${(3 x)}^{2} \cdot (3 x y)$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) x^{3} y} + x \sqrt{48 x y}$

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

$\sqrt{3^{2} \cdot 3 x^{3} y} + x \sqrt{48 x y}$

Factor out $x^{2}$ .

$\sqrt{3^{2} \cdot 3 (x^{2} x) y} + x \sqrt{48 x y}$

Move $3$ .

$\sqrt{3^{2} x^{2} \cdot 3 x y} + x \sqrt{48 x y}$

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

$\sqrt{{(3 x)}^{2} \cdot 3 x y} + x \sqrt{48 x y}$

Add parentheses.

$\sqrt{{(3 x)}^{2} \cdot 3 (x y)} + x \sqrt{48 x y}$

Add parentheses.

$\sqrt{{(3 x)}^{2} \cdot (3 x y)} + x \sqrt{48 x y}$

Pull terms out from under the radical.

$3 x \sqrt{3 x y} + x \sqrt{48 x y}$

Rewrite $48 x y$ as ${(2^{2})}^{2} \cdot (3 x y)$ .

Factor $16$ out of $48$ .

$3 x \sqrt{3 x y} + x \sqrt{16 (3) x y}$

Rewrite $16$ as $4^{2}$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

$3 x \sqrt{3 x y} + 2^{2} x \sqrt{3 x y}$

Raise $2$ to the power of $2$ .

$3 x \sqrt{3 x y} + 4 x \sqrt{3 x y}$

Add $3 x \sqrt{3 x y}$ and $4 x \sqrt{3 x y}$ .

$7 x \sqrt{3 x y}$