Question

assuming x and y are both positive, write the following expression in simplest radical form.
$x\sqrt{54x^{4}y^{4}}$

Explanation:

Step1: Factor radicand into perfect squares

$x\sqrt{9 \cdot 6 \cdot x^4 \cdot y^4} = x\sqrt{9x^4y^4 \cdot 6}$

Step2: Simplify the perfect square root

$x \cdot 3x^2y^2 \cdot \sqrt{6}$

Step3: Multiply like terms outside radical

$3x^{1+2}y^2\sqrt{6} = 3x^3y^2\sqrt{6}$

Answer:

$3x^3y^2\sqrt{6}$