Calculate sqrt(60x)*sqrt(12x)*sqrt(63x)*sqrt(42x). Express your answer in simplest radical form in terms of x. Note: When entering a square root with more than one character, you must use parentheses or brackets. For example, you should enter sqrt(14) as "sqrt(14)" or "sqrt{14}".
+2668 https://web2.0calc.com/questions/algebra-question_120#r1. I answered the question here
+1223 \(\sqrt{60x} \cdot \sqrt{12x} \cdot \sqrt{63x} \cdot \sqrt{42x}\)
\(= \sqrt{60x \cdot 12x \cdot 63x \cdot 42x}\)
\(= \sqrt{(2^2 \cdot 3 \cdot 5) \cdot (2^2 \cdot 3) \cdot (3^2 \cdot 7) \cdot (2 \cdot 3 \cdot 7) \cdot x^4}\)
\(= \sqrt{2^5 \cdot 3^5 \cdot 5 \cdot 7^2 \cdot x^4}\)
\(= 2^2 \cdot 3^2 \cdot 7 \cdot x^2 \cdot \sqrt{2 \cdot 3 \cdot 5}\)
\(= \boxed{252x^2 \sqrt{30}}\)
tl;dr: split each number into their prime factors, multiply them all, then move the perfect squares outside the square root
