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S. from Utah asks, "Why do math teachers make us simplify radical expressions?"
Great question, S! The good news is, we have a unit on "Simplifying Radical Expressions" in our reference section, and the unit has a page that answers your question! If you visit this page right here: Why We Simplify Radicals, you'll get an explanation for some of the reasons.
The short answer is: There are multiple ways of writing the same number, but if we all follow the simplification rules, we'll all write our answers the same way, which makes it easier for people to work together, if they're all expressing their work in the same way.
Here's another way of looking at it: suppose you lived at 12 Main Street. Which of the following pieces of mail are addressed to you?
- 12 Main St
- SQR(144) Main St
- 2SQR(36) Main St
- 4SQR(9) Main St
- 3SQR(16) Main St
- SQR(9)SQR(16) Main St
Which of these pieces of mail are addressed to you? Well, obviously the first one is, but even though the others might not look like it, they all actually evaluate to 12 Main St. But the big question is: how many of them will actually get delivered to you? The answer is probably, "It depends on how much of a sense of humor the postal workers have!"
The reality is, if we don't simplify our answers so they all look the same, we make a lot of extra work for someone. Right now, that someone is your teacher (who has to grade your tests and homework), but if you pursue a career in a STEM field, the someone will be you, and the people on your team.
So practice simplifying those radicals until it becomes second nature. Your teacher will thank you now, and someday future-you may thank you as well!