1. By: Taylor Schultz MATH 3911

2.  George Polya was a teacher and mathematician.  Lived from 1887-1985  Published a book in 1945: How To Solve It, explaining that people could learn to become better problem solvers.

3.  1. Understand the problem.  2. Devise a plan.  3. Carry out the plan.  4. Look back.

4.  Find the square root of 1,444 without using a calculator.  √1,444

5.  When first looking at a problem, you must first read the problem carefully and see if you understand it.  Ask yourself, what do you know, and what do you want to figure out?  We know that: A number b is a square root of a number a if b 2 = a.  In order to find a square root of a, you need a # that, when squared, equals a.  We want to figure out: What number squared would equal 1,444.  (b 2 = 1,444)

6.  For this second step, you need to develop a strategy for using what you know.  Consider how the problem relates to concepts you know or other problems you have solved.  You can solve this problem by using a guess- and-check (trial and error) approach, or by using an algebraic square root method.

7.  So, how do we find the square root?  IT’S EASY!  Just ask what times itself is the number in the root symbol?  Examples:  √9 is 3 because 3 times 3 is 9 ( 3×3=9)  √16 is 4 because 4 times 4 is 16 ( 4×4=16)  √49 is 7 because 7 times 7 is 49 (7×7=49)

8.  This strategy requires you to start by making a guess and then checking how far off your answer is.  Then, you revise your guess and try again!  So, we want to know what the b is in b 2 = 1,444.  Plan: Find what b is to equal 1,444. (b×b=1,444)

9.  This is the step where you carry out the steps of your plan.  We have came up with the guessing and checking method, so let’s put it to use!

10.  You could start by multiplying any of the two same numbers together.  Let’s try: 20×20, which equals 400.  This answer is obviously way lower than 1,444, so I’ll revise my guess and try again.  This time I’ll try: 30×30, which equals 900.  This answer is still too low, but I am getting closer.  This time I’ll try 34×34, which equals 1,156.  I am still not quite there, but I am getting closer.  I have now started to narrow down my guesses, so this time I’ll try 38×38, which equals 1,444!  Through guessing and checking, I have now figured out that b=38 ( 38 2=1,444 )

11.  Finally, in this last step you look back reviewing and checking your results.  Have you answered the original question?  Yes, we have answered that the √1,444=38.  Is there a way to check your answer to see if it is reasonable?  Yes, by multiplying 38×38 to equal 1,444.  Also, if you have a calculator, you can plug in the √1,444 giving you 38.  You can use this knowledge to solve related problems in the future.