Question

radical expressions
65
x√x²
simplify
?

Explanation:

Step1: Simplify the square root

Recall that $\sqrt{x^2} = |x|$, but if we assume $x\geq0$ (since the expression might be defined for non - negative real numbers in a basic context), then $\sqrt{x^2}=x$.

Step2: Multiply with the outer x

Now we have $x\times\sqrt{x^2}$, and since $\sqrt{x^2} = x$ (for $x\geq0$), we multiply $x$ and $x$. Using the rule of exponents $a^m\times a^n=a^{m + n}$, here $a = x$, $m=1$, $n = 1$, so $x\times x=x^{1 + 1}=x^2$.

Answer:

$x^2$ (assuming $x\geq0$; if we consider all real numbers, the simplification is $x|x|$)