Tutoring high school math, radicals are prominent. The math tutor introduces addition and subtraction of them.
Adding radicals is much like adding variables. Note that x=1x; the 1 is understood to be there, but never written. Similarly, √3=1√3. Therefore, 2√5 + √5 = 3√5
You can’t simplify x plus y; x+y is just x+y. Similarly, √6+√7 doesn’t simplify. A calculator will give you a decimal for it, but that’s not an exact value.
So what about the following:
Example 1: Simplify √(12)+√(75)+√3
You may want to read up on simplifying radicals in my earlier post to understand what follows.
Solution: On the face of it, we can’t add the radicals because they’re not the same kind. However, we can simplify some of them as follows:
√(12) = 2√3
√(75) = 5√3
Simplifying reveals them to be the same kind. We indeed can add them.
2√3 + 5√3 + √3 = 8√3
By a similar principle, √(50)-√8=5√2-2√2=3√2
I’ll be covering some different examples in an upcoming post:)
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.