Rewrite expressions with radicals and rational exponents using exponent properties.
Solve equations of the form x^(m/n) = k in real numbers
Problem
Solve \(x^{1/2}=5\) over the real numbers by undoing the square root, then verify the domain of the principal root.
Big Picture
What this problem is really about
The one-half power is a principal square root, so its output and real radicand are nonnegative. We’ll rewrite the equation in radical form, square both sides under those valid conditions, test the candidate in the original equation, and explain why no negative companion solution belongs.
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