PROBLEMS AND SOLUTIONS - OPERATIONS ON IRRATIONAL NUMBERS

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1 PROBLEMS AND SOLUTIONS - OPERATIONS ON IRRATIONAL NUMBERS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to Thank you! PLEASE NOTE THAT YOU CANNOT USE A CALCULATOR ON THE ACCUPLACER - ELEMENTARY ALGEBRA TEST! YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR! Problem 1: "simplify." Here we are asked to "simplify" instead of finding the square root. Problem 2: "simplify." Here we are asked to "simplify" instead of factoring out perfect-square factors. Problem 3: Problem 4: Problem 5: Problem 6:

2 Problem 7: factors out of the sum. Problem 8: Problem 9: Combine the "like" radicals in possible. and simplify, if factors out of the result Problem 10: factors out of the difference. Problem 11: Problem 12: Problem 13: Please note that there is an implied coefficient of 1 in front of write it. However, it must be used in addition and subtraction!. It is NOT customary to

3 Problem 14: Problem 15: factors out of the product. Problem 16: Problem 17: Problem 18: Problem 19: Problem 20: Please note that the two middle products have like radicands that is why we added their coefficients! Problem 21:

4 Problem 22: factors out of the quotient. Problem 23: Problem 24: Problem 25: Problem 26: Problem 27: Problem 28: Problem 29:

5 Problem 30: SOLUTIONS You can find detailed solutions below the link for this problem set! No simplification can take place. The only thing that could be done is to change the radical to a rounded decimal number and then subtract. 11. No simplification can take place. The only thing that could be done is to change the radicals to rounded decimal numbers and then subtract

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