Example of the squaring both sides canceling each other show working please

Question

ScanSolve AI Tutor · Accepted Answer

Here's an example showing how squaring a square root cancels each other out:

Let's consider the expression $(\sqrt{x})^2$ .

Recall the definition of a square root.
The square root of a number $x$ can be written as $x$ raised to the power of $\frac{1}{2}$ . This is valid for $x \ge 0$ .
$\sqrt{x} = x^{\frac{1}{2}}$
Substitute this definition into the expression.
$(\sqrt{x})^2 = \left(x^{\frac{1}{2}}\right)^2$
Apply the exponent rule $(a^m)^n = a^{m \cdot n}$ .
Here, $a=x$ , $m=\frac{1}{2}$ , and $n=2$ .
$\left(x^{\frac{1}{2}}\right)^2 = x^{\frac{1}{2} \times 2}$
Multiply the exponents.
$x^{\frac{1}{2} \times 2} = x^1$
Simplify the expression.
$x^1 = x$
So, the working shows:
$\boxed{(\sqrt{x})^2 = x}$
This property holds true for any non-negative number $x$ .

Answer