Question

simplify \\(\sqrt{x^4 y^2}\\)

Explanation:

Step1: Recall square root property

The square root of a product is the product of the square roots, i.e., $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ for $a,b\geq0$. Also, $\sqrt{x^n}=x^{\frac{n}{2}}$ when $x\geq0$.

Step2: Apply to $\sqrt{x^4y^2}$

First, split the square root: $\sqrt{x^4y^2}=\sqrt{x^4}\cdot\sqrt{y^2}$.
For $\sqrt{x^4}$, using $\sqrt{x^n}=x^{\frac{n}{2}}$, we have $x^{\frac{4}{2}} = x^2$.
For $\sqrt{y^2}$, we have $y^{\frac{2}{2}} = y$ (assuming $y\geq0$ for simplicity, or we can write $|y|$, but if we consider non - negative variables, it's $y$).
So $\sqrt{x^4y^2}=x^2y$.

Answer:

$x^{2}y$