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"radical challenge" is correct and usable in written English.
This phrase pretty much means anything that goes against the status quo or the accepted way of doing things, and so it can be used in a variety of contexts. For example, "Many people are pushing for a radical challenge to the current educational system."
Exact(48)
And it's that which is feminism's most radical challenge.
Kawakubo's most radical challenge to the canons of Western tailoring lay in her cutting.
The proposal does constitute a radical challenge to the philanthropic status quo.
But few historians would describe his presidency as a radical challenge to the status quo.
Their politics, although a radical challenge to the conventional wisdom, have never been of the left.
The play marks a radical challenge to Shakespeare's infamous Jewish fantasy figure of Shylock.
Similar(11)
Let me tell you: this may be the most radical, challenging film ever made.
"Uncertain", "radical", "challenging", and even "nostalgic" are some of the words that will be thrown around.
By thwarting the elected Parliament, Mr. Khamenei mocks democratic principles and invites more radical challenges to clerical rule in the future.
"Sesame Street" and "The Muppet Show," which began as radical challenges to the children's education status quo, have become synonymous with cultural wholesomeness and normalcy.
The primary purpose of foreign aid, as it has been since its conception after World War II by European nations hoping to bind their colonies to them in fact if not name, is to maintain the military and economic power of the rich nations by buying cooperation and forestalling state failure and radical challenges.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com