Choose x, a positive whole number. You will be determining r, the square root of x. Sometimes r is an irrational number. For example when asked the square root of the number five, your answer will be "root five."
Break x down into prime integers. The simplest way to do this is to divide multiples of five by five, other odd numbers by three and other even ones by two. You will end up with a list of prime integers, which yield x when multiplied together. For example, consider the number 110. Dividing by five yields 22. Twenty-two divided by two is 11. Since 11 is not divisible by three, the square root of 110 is "root five times two times 11," an irrational number.
Find the principal square root of x. In algebra you will first deal with rational numbers. Numbers with square roots that are rational numbers are called perfect squares. For the number 81, dividing by three yields 27 and doing so again yields nine. Divide one last time by three to get three. The prime integers that multiply to equal 81 are three, three, three and three. By pairing these integers you get (3x3)(3x3) or 9x9. The square root of 81 is therefore nine.
Show your work. In algebra, as with most classes, problems will be easy at first then increase in difficulty. By practicing writing the reduction of x into prime integers then determining the square root r for simple tasks like finding the square root of four (2 x 2= 4, making the answer 2), you'll be better prepared for complex problems that require many steps.