Question

simplify. assume that all variables are positive.
\sqrt{48x^{7}}

\sqrt{48x^{7}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Factor into perfect squares

$\sqrt{16 \times 3 \times x^6 \times x}$

Step2: Split radical into products

$\sqrt{16} \times \sqrt{3} \times \sqrt{x^6} \times \sqrt{x}$

Step3: Simplify perfect square roots

$4 \times \sqrt{3} \times x^3 \times \sqrt{x}$

Step4: Combine like terms

$4x^3\sqrt{3x}$

Answer:

$4x^3\sqrt{3x}$