Question

xpressions
25 100%
\sqrt{a^{3}b^{2}}
?

Explanation:

Step1: Simplify the square root

We can use the property of square roots $\sqrt{xy}=\sqrt{x}\cdot\sqrt{y}$ (where $x\geq0,y\geq0$) and $\sqrt{x^{n}} = x^{\frac{n}{2}}$ for non - negative $x$.
First, split the square root: $\sqrt{a^{3}b^{2}}=\sqrt{a^{2}\cdot a\cdot b^{2}}$.

Step2: Apply the square root property

Using $\sqrt{x^{2}} = |x|$ (for real numbers) and $\sqrt{x^{n}}=x^{\frac{n}{2}}$:
$\sqrt{a^{2}\cdot a\cdot b^{2}}=\sqrt{a^{2}}\cdot\sqrt{a}\cdot\sqrt{b^{2}}$.
Since for non - negative real numbers (assuming $a\geq0,b\geq0$ for simplicity in the context of simplifying algebraic expressions), $\sqrt{a^{2}} = a$ and $\sqrt{b^{2}}=b$.
So $\sqrt{a^{2}}\cdot\sqrt{a}\cdot\sqrt{b^{2}}=a\cdot b\cdot\sqrt{a}=ab\sqrt{a}$.

Answer:

$ab\sqrt{a}$