With homework ? not asking for answers, but want to learn how to do these. simplify

Hi there!

Since you said that you didn't want answers, I'll try my best to just explain things to you. However, if you'd like to work on problems, just let me know and I'd be happy to help you find answers.

SIMPLIFY THE SUM OR DIFFERENCE:
For these, what you can do is get all of the numbers to the same form. Such as simplifying the square root of 64 to 8. This will help you to be able to add or subtract things easily. The only time that you can subtract or add things is if whatever is under the square root is the same.

SIMPLIFY THE PRODUCT:
For these, you need to first multiply or distribute. You multiply both the numbers and the square roots. However, what is under the square root stays underneath the square root until you simplify it.

SIMPLIFY THE QUOTIENT:
These can be tricky sometimes. What you need to do is first, get the top and bottom as simplified as you can. Then, begin getting rid of the same things, as they cancel each other out. Once you've simplified as much as you can, make sure there isn't a square root in the denominator. There should never be one there! To get rid of it, multiply the top and bottom by whatever is under the square root on the bottom. For example, if I had 5/squareroot(10), then I would multiply the top and bottom by squareroot(10) to get rid of the square root in the denominator.

SIMPLIFY THE EXPRESSION:
To simplify the expression, most times all you need to do is distribute and possibly subtract or add (sometimes). The only time you can add or subtract square root is if (what is under the square root) is the same. If they are not the same, then you do not need to worry about further simplifying as there is nothing else that you can do.

Hope this helps!! :)
Message me anytime if there's anything else that I can help you with!

    So the given pair has (a) infinitely many solutions.

Step-by-step explanation: