Simplify the Radical Expression square root of 75x^2y

$\sqrt{75 x^{2}} y$

Rewrite $75 x^{2}$ as ${(5 x)}^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) x^{2}} y$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 3 x^{2}} y$

Move $3$ .

$\sqrt{5^{2} x^{2} \cdot 3} y$

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

$\sqrt{{(5 x)}^{2} \cdot 3} y$

Pull terms out from under the radical.

$| 5 x | \sqrt{3} y$

Remove non-negative terms from the absolute value.

$5 | x | \sqrt{3} y$