Surds are rarely mentioned in today's school curriculum. But I did remember my father mentioning to me with a great joy. It was not in my school curriculum (back in 1970's), but was able to get old mathematics book and learn about Surds. Recently, I rediscovered the Surds when teaching mathematics to my early teen daughters. They got the hang of it and loved it.
Take the example for simplifying the following (so that there there are no irrational numbers in the denominator):

Take the example for simplifying the following (so that there there are no irrational numbers in the denominator):

It involves:
Here are some links that you can give your 13-15 year olds to practice on Surds:
Interestingly the links is from the Austrailia! They still teach Surds. You can get additional links by searching goggle with key words "Surds site:au" (site:au will filter your search for the URL that ends with .au which is Australia)
So have fun and make the kids of the world smarter!
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