Simplify x square root of y^3+ square root of x^2y^5-5x square root of y^7

$x \sqrt{y^{3}} + \sqrt{x^{2} y^{5}} - 5 x \sqrt{y^{7}}$

Step 1

Factor out $y^{2}$ .

$x \sqrt{y^{2} y} + \sqrt{x^{2} y^{5}} - 5 x \sqrt{y^{7}}$

Step 2

Pull terms out from under the radical.

$x (y \sqrt{y}) + \sqrt{x^{2} y^{5}} - 5 x \sqrt{y^{7}}$

Step 3

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

Factor out $y^{4}$ .

$x y \sqrt{y} + \sqrt{x^{2} (y^{4} y)} - 5 x \sqrt{y^{7}}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$x y \sqrt{y} + \sqrt{x^{2} ({(y^{2})}^{2} y)} - 5 x \sqrt{y^{7}}$

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

$x y \sqrt{y} + \sqrt{{(x y^{2})}^{2} y} - 5 x \sqrt{y^{7}}$

Step 4

Pull terms out from under the radical.

$x y \sqrt{y} + x y^{2} \sqrt{y} - 5 x \sqrt{y^{7}}$

Step 5

Rewrite $y^{7}$ as ${(y^{3})}^{2} y$ .

Factor out $y^{6}$ .

$x y \sqrt{y} + x y^{2} \sqrt{y} - 5 x \sqrt{y^{6} y}$

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

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

Step 6

Pull terms out from under the radical.

$x y \sqrt{y} + x y^{2} \sqrt{y} - 5 x y^{3} \sqrt{y}$