Final answer:
To simplify the expression √2a· √14a³· √5a, multiply the numbers inside the square roots and then remove any perfect squares. The simplified expression is 2a^2√(35a).
Step-by-step explanation:
To simplify the expression √2a· √14a³· √5a, we can multiply the numbers inside the square roots and then remove any perfect squares. First, let's multiply the numbers inside the square roots: √(2a) * √(14a³) * √(5a). This gives us the expression √(2a * 14a³ * 5a). Next, let's simplify the expression inside the square root: √(2a * 14a³ * 5a) = √(140a^5). Finally, we can remove the perfect square from inside the square root: √(140a^5) = √(2^2 * 2 * 5 * 7 * a^4 * a) = 2a^2√(35a).