simplify.\nremove all perfect squares from inside the square root.\n$\\sqrt{52x^{4}}=$

Explanation:

Step1: Factorize the number inside the square root

Factorize (52) into (4\times13), and (x^{4}) into ((x^{2})^{2}). So (\sqrt{52x^{4}}=\sqrt{4\times13\times(x^{2})^{2}}).

Step2: Use the property (\sqrt{ab}=\sqrt{a}\cdot\sqrt{b})

(\sqrt{4\times13\times(x^{2})^{2}}=\sqrt{4}\cdot\sqrt{(x^{2})^{2}}\cdot\sqrt{13}). Since (\sqrt{4} = 2) and (\sqrt{(x^{2})^{2}}=\vert x^{2}\vert=x^{2}) (because (x^{2}\geq0) for all real (x)).

Step3: Calculate the result

(2\cdot x^{2}\cdot\sqrt{13}=2x^{2}\sqrt{13}).

Answer:

(2x^{2}\sqrt{13})