Question

simplify.
remove all perfect squares from inside the square root. assume ( x ) is positive.
( sqrt{54x^7} = square )

Explanation:

Step1: Factor into perfect squares

$\sqrt{54x^7} = \sqrt{9 \times 6 \times x^6 \times x}$

Step2: Separate perfect square factors

$\sqrt{9} \times \sqrt{x^6} \times \sqrt{6x}$

Step3: Simplify perfect square roots

$3 \times x^3 \times \sqrt{6x}$

Step4: Combine terms

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

Answer:

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