What are different ways to figure out the square roots of a number?

Expert Answers
Ashley Kannan eNotes educator| Certified Educator

If the question is asking how to determine the square roots of a number, the most elemental way that is dominant in today's classroom is the use of a calculator.  In most settings the use of a calculator for computational issues such as finding a square root has become accepted practice.  There can be a healthy debate as to whether this helps to child, but the fact of the matter is that math curriculums are embracing so many different approaches to solving problems and advocating applications which involve higher ordered thinking. Computation has become a part of the process of advanced mathematics instruction and thus using a calculator has become quite standard and accepted practice.

If one were to try to find square roots without a calculator, one of the most time honored of systems is the "guess and check" approach.  In this, you simply keep plugging away until you find an answer that works.  It is not the most time efficient means of solving, but it does get the job done and does help you find a square root of a number. For example, if you wanted to find the square root of 8, guess and check means that you find a range of numbers from which to work. Squaring 2 gives you 4, and squaring the next number is 3 gives you 9.  With that, you have your range.  We know that 2 is too small and 3 is too large.  Thus, the answer exists between both numbers.

Since 9 is closer to 8 than it is to 4, we can narrow down some of our options to work with the upper half of the bracket.  This means that we can start by taking 2.5 and squaring that, giving us 6.25.  Close, but we need to continue progressing.  Taking the next increment of 2.6, we square that and get 6.76. Continuing on to squaring 2.7, we can get to 7.29, which is closer. This process continues on in the same manner until we get to 2.9, when we go over because 2.9 squared gives 8.41.  Thus, guess and check has helped us narrow that the square root of 8 exists between 2.8 and 2.9.  To further narrow it to specific decimal points, the process would be continued accordingly. Guess and check is another way of being able to do and figure out square roots without the use of a calculator.

jess1999 | Student

Of course the most easiest way to find a square root of number is to be able to use a calculator . If you are unable to use a calculator though , you are still able to find the square root of a number if you are able to know your multiplication . For example square root 144 would be 12 because you would know that 12 X 12 is 144 . But if it's not an evenly multiplied number such as the squared root of 45 you would have to make an estimate . You know that the 7 X 7 = 49 and that 6 X 6 = 36 , therefore you would know that the number is between 6 and 7 . Usually though math teachers would just tell the students to leave it in square root form if you are unable to simplify it any further .