Spacing under square root

When TeX is in display-math mode, the numerator and denominator of a fraction are rendered in text style. If you want to apply text style to other material in a display-math environment, you need to provide the directive textstyle explicitly.

documentclass{article} 
begin{document}
[ % start an unnumbered display math group
sqrt{k^2_t-k^2} qquad
{textstylesqrt{k^2_t-k^2}} qquad
frac{sqrt{k^2_t-k^2}}{1}
]
end{document}

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Addendum to address a follow-up comment by @mavzolej, who claims that inserting the textstyle instruction doesn't "work" if the expression inside the square root term contains langle (and rangle too, presumably). Unfortunately, he/she didn't provide compilable code to demonstrate the correctness of the claim. For sure, changing sqrt{k^2_t-k^2} to sqrt{langle k^2_t-k^2rangle} does not imply that imposing textstyle won't succeed in reducing the overall size of the square root term:

documentclass{article}
newcommandstuff{sqrt{langle k^2_t-k^2rangle}}
begin{document}
$displaystylestuff quadmbox{vs.}quad textstylestuff$
end{document}