Solve {left(x*sqrt{y/x}right)}^2

$${ \left(x \times \sqrt{ \frac{ y }{ x } } \right) }^{ 2 }$$

Evaluate

$$xy$$

Solution Steps

Expand \left(x\sqrt{\frac{y}{x}}\right)^{2}.

$$x^{2}\left(\sqrt{\frac{y}{x}}\right)^{2}$$

Calculate \sqrt{\frac{y}{x}} to the power of 2 and get \frac{y}{x}.

$$x^{2}\times \frac{y}{x}$$

Express x^{2}\times \frac{y}{x} as a single fraction.

$$\frac{x^{2}y}{x}$$

Cancel out x in both numerator and denominator.

$$xy$$

Expand

$$xy$$

Solution Steps

Expand \left(x\sqrt{\frac{y}{x}}\right)^{2}.

$$x^{2}\left(\sqrt{\frac{y}{x}}\right)^{2}$$

Calculate \sqrt{\frac{y}{x}} to the power of 2 and get \frac{y}{x}.

$$x^{2}\times \frac{y}{x}$$

Express x^{2}\times \frac{y}{x} as a single fraction.

$$\frac{x^{2}y}{x}$$

Cancel out x in both numerator and denominator.

$$xy$$