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The phrase "are extremely rigorous" is correct and usable in written English.
It can be used to describe something that is very strict, thorough, or demanding, often in the context of standards, processes, or evaluations.
Example: "The academic requirements for this program are extremely rigorous, ensuring that only the most dedicated students succeed."
Alternatives: "are highly demanding" or "are very strict".
Dictionary
are extremely rigorous
adverb
To an extreme degree
synonyms
Exact(2)
"We are extremely rigorous in our methodology and we are constantly challenging ourselves to be more exacting," said Turner.
As these qualifying exams are extremely rigorous, support is usually available to people progressing through the exams.
Similar(56)
"Michael was extremely rigorous," says Fiennes, who watched him rehearse and perform at close range.
You will see when you watch the show that it's extremely rigorous.
The most widely used and least convincing is that the accession process was extremely rigorous.
But on the inside you have to be extremely rigorous to reduce that to a minimum.
All these tests are objective tests that can be tested factually rather than subjective ones, so it's extremely rigorous".
Most experts agree the new child care study, the largest of its kind ever conducted, is extremely rigorous.
Even when there's this kind of loose, open sense to it -- that's really her expertise in terms of handling paint -- the process is extremely rigorous and planned".
The exhibition, according to the Tate curator Matthew Gale, will seek to "redress the idea that he was a quirky artist, allowing his cat to paint, but rather show that he was extremely rigorous, with a clear sense of how his work was progressing... and it will give a sense of the extraordinary variety of his production".
Hicks said: "All the evidence does suggest that it does work and we have been extremely rigorous in putting together our list, making sure there is an evidence base for each book – that they have been used and found to be effective".
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com