Simplify square root of (5x^2y^2)/4+ square root of 5x^2y^2

$\sqrt{\frac{5 x^{2} y^{2}}{4}} + \sqrt{5 x^{2} y^{2}}$

Step 1

Simplify each term.

Rewrite $\frac{5 x^{2} y^{2}}{4}$ as ${(\frac{x y}{2})}^{2} \cdot 5$ .

Factor the perfect power ${(x y)}^{2}$ out of $5 x^{2} y^{2}$ .

$\sqrt{\frac{{(x y)}^{2} \cdot 5}{4}} + \sqrt{5 x^{2} y^{2}}$

Factor the perfect power $2^{2}$ out of $4$ .

$\sqrt{\frac{{(x y)}^{2} \cdot 5}{2^{2} \cdot 1}} + \sqrt{5 x^{2} y^{2}}$

Rearrange the fraction $\frac{{(x y)}^{2} \cdot 5}{2^{2} \cdot 1}$ .

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

Pull terms out from under the radical.

$\frac{x y}{2} \sqrt{5} + \sqrt{5 x^{2} y^{2}}$

Combine $\frac{x y}{2}$ and $\sqrt{5}$ .

$\frac{x y \sqrt{5}}{2} + \sqrt{5 x^{2} y^{2}}$

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

Move $5$ .

$\frac{x y \sqrt{5}}{2} + \sqrt{x^{2} y^{2} \cdot 5}$

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

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

Pull terms out from under the radical.

$\frac{x y \sqrt{5}}{2} + x y \sqrt{5}$

Step 2

To write $x y \sqrt{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x y \sqrt{5}}{2} + x y \sqrt{5} \cdot \frac{2}{2}$

Step 3

Simplify terms.

Combine $x y \sqrt{5}$ and $\frac{2}{2}$ .

$\frac{x y \sqrt{5}}{2} + \frac{x y \sqrt{5} \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{x y \sqrt{5} + x y \sqrt{5} \cdot 2}{2}$

Step 4

Simplify the numerator.

Move $2$ to the left of $x y \sqrt{5}$ .

$\frac{x y \sqrt{5} + 2 \cdot (x y \sqrt{5})}{2}$

Add $x y \sqrt{5}$ and $2 x y \sqrt{5}$ .

$\frac{3 x y \sqrt{5}}{2}$