Use the product property of roots to choose the expression equivalent to 3√5x*3√25x^2? √30x3√125x33√30x^26√125x^3

Answer: [tex]\sqrt[3]{125x^3}[/tex].
Step-by-step explanation: Given radical expression [tex]\sqrt[3]{5x} \times \sqrt[3]{25x^2}[/tex].According to the product property of roots.[tex]\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{a \times b}[/tex]On applying above rule, we get [tex]\sqrt[3]{5x} \times \sqrt[3]{25x^2} = \sqrt[3]{5x \times 25x^2}[/tex]5 × 25 = 125 and [tex]x \times x^2 = x^3[/tex]Therefore,[tex]\sqrt[3]{5x \times 25x^2}= \sqrt[3]{125x^3}[/tex]So, the correct option would be second option [tex]\sqrt[3]{125x^3}[/tex].