The square root function is one of the basic functions people learn on the algebraic level. When considering square root one should ask themselves one question ‘What positive number times itself makes this’. Some may think why does it have to be a positive number? This is because in science usually the negative sign just implicates direction and people want the simplest answer so why bother write the negative sign when it’s not needed. Now that we know some of the basics of a square root let’s look at some examples.
What is the square root of 4? When we look at this we think 2*2 = 4 so 2 is the square root of 4. This may be obvious but lets work with a little less of an obvious example… What is the root of 169? First we would estimate the general root by thinking 10*10= 100 and 15*15=225 so the square root must be somewhere between 10 and 15. Let’s try 13; 13*13=169 so that means the square root of 169 is 13.
Many people have memorized their multiplication tables and memorizing perfect squares is just the same. People just remember the list of perfect squares as 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225 etc. This list can also be re-written as 1*1=1,2*2=4,3*3=9 and etc. This list can be very useful because when practicing basic problems in math class you will most likely be working with these easy numbers because your teacher wants to make the work simple and easy to understand so you can memorize it faster.
Now let’s think what if we try and take the square root of a number that is not a whole number. For example what is the square root of 6? If we pull out a calculator we will find that it is 2.449489… This is easy when we have a calculator but how can we do it when we do not have this luxury. We would have to use our ‘in between’ method that we used earlier. We would have to think 2^2=4 and 3^2=9; 6 is between 4 and 9 so our square root is between 2 and 3. Let’s try 2.5; 2.5^2=6.25 which is pretty close but too high let’s try 2.4; 2.4^2=5.76 and 6 is between 5.76 and 6.25 so our number is between 2.4 and 2.5. Just to be a little more precise let’s find it even closer by trying 2.45; 2.45^2=6.0025 which is very close to 6 so let’s say the square root of 6 is roughly 2.45.
That work can be very annoying when you do not have a calculator in hand so let’s focus on square roots themselves and not all of the mundane work in between. What are the different ways we can express the square root of something? We have the radical √x and we have x^0.5 where x is some number. Some may ask ‘why we raise something to the half’ this is because square rooting a number is the opposite of squaring a number (x^2); and the reciprocal (opposite) of 2 is ½ or 0.5. This also introduces a bunch of other things like cube root which is simply x^(1/3) . In fact we can use this principle for many different power related problems but hopefully you were able to further understand what a square root really is and how you can find them.
