Ways & How

how to work out square roots

how to work out square roots

A square root is a mathematical term that can be explained by ?x = r, where r is the square root of x. In other words, the square root of a number x is the number r, which when multiplied by itself, equals x. For example, to keep it simple for now, the square root of 4 is 2 because when you multiply 2 by itself (2 x 2), you get 4. But it isn’t always that simple, especially because not every number has a simple square root. This is why it can be helpful to learn how to work out square roots. When we talk about square roots in standard math, we are usually only dealing with the square roots of positive numbers as negative numbers do not have regular square roots. The square root of a negative number can only be discussed within the framework of complex numbers because a negative number multiplied by itself always equals a positive number. This also means that every positive number has two square roots, one positive and one negative. So to be more accurate in the above example, the square roots of 4 are both 2 and -2. When you are dealing with numbers that aren’t perfect squares like 4, you will always end up with an irrational number.



ere are some ways to solve square roots:

  1. Check if the number is a perfect square like 1, 4,9,16,25,36,49,64,81,100,121, etc. If so, check your answer by multiplying by itself to see if you get the original question. For instance, it is easy to figure out that the square root of 25 is 5, but to be completely sure, we can multiply 5 x 5 to verify our answer. Since 5 x5 is 25, then we know for sure that 5 is the square root of 25.

  2. Now when you are given a number that isn’t a perfect square, it’s time to try the guess and check technique. This is appropriate when you are working with smaller numbers. For example, you are asked what is the ?20. First, find out the two nearest perfect squares. In this case, the nearest are 16 and 25, which have square roots of 4 and 5, respectively. It is clear then that the answer is between 4 and 5. Now try guessing and multiplying numbers between 4 and 5 by themselves. Try 4.1 x 4.1, 4.2 x 4.2, and so on. For ?20, the nearest possible square root is 4.4.

  3. The last and the easiest way to get the square root of any numbers is to use good old calculator. Just input the problem to get the answer.

There are also other ways in finding square roots, but you may want to understand the concept and basics first before learning more complex methods.  When you finally get the hang of how to work out square roots, solving them will be a breeze, and who knows, you might be a math wizard someday!

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