Question

simplify.
\sqrt{2x}\cdot\sqrt{7x}
assume that the variable represents a positive real number.

Explanation:

Step1: Use the property of square roots $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$

$\sqrt{2x}\cdot\sqrt{7x}=\sqrt{(2x)\cdot(7x)}$

Step2: Multiply the terms inside the square root

$(2x)\cdot(7x) = 14x^2$, so we have $\sqrt{14x^2}$

Step3: Simplify the square root of $x^2$ (since $x$ is positive, $\sqrt{x^2}=x$)

$\sqrt{14x^2}=x\sqrt{14}$

Answer:

$x\sqrt{14}$