How Decimal Number System Works

The decimal number system is an elegant way of representing quantities using a system of digits and place values. When you understand how the system is put together, you’ll be able to use it in different ways.  Continue reading “How Decimal Number System Works”

How to Find the Square Root of a Number

We mentioned before that when you square a number, you’ll get a square number or a perfect square. You can use the perfect square to find out what numbers were multiplied together to get the perfect square. The process of using the perfect square to get back to those numbers is finding the square root of a number. For example, 3 * 3 = 3^2 = 9. 9 Here is perfect square. You can take the square root of 9 to get back to 3. You can see that squaring a number and taking the square root of the result are actually inverse processes. Continue reading “How to Find the Square Root of a Number”

Square Root Function

If you multiply any integer except for 0 by itself, you’ll get a positive perfect square. For example, 3 * 3 = 9 or you can write the same expression as 3^2 = 9. Now, if you have the number 9, knowing that 4 is a perfect square and want to know what number was raised to the second power or multiplied by itself to get the 9, you need a function that takes you from the perfect square back to the number. That function is called the “square root function.” That means,

3 * 3 = 9 Or 3^2 = 9, then, sqrt(9) = 3. Continue reading “Square Root Function”

Calculating Square of Large Numbers

Calculating the square of numbers like 8, 9, etc., is easy but calculating the square of a number like 105 without using a calculator.

There is an interesting way to calculate the square of large numbers like 255 without using a calculator. It’s probably not easy to do it in your mind but you can do it on a piece of paper. It’s essentially a way to calculate the square root of numbers that have a 5 in 1’s place value. It does not matter what sort of digits you might have in the other place values but the 1’s place value has to be a 5.

Click to see how to derive the formula

So the formula will be (x5)^2 = x(x+1)100 + 25

The formula above was derived for a 2-digit number but it can be used for any number with any number of digits provided that the number has a 5 in the 1’s place. For example, if you were to calculate 115^2, you’d simply use the formula as follows:

115^2 = 11(12)100 * 25 = 13225

You can learn how this formula was created and based on that, you can create any sort of formula for any kind of situation you might find yourself in.

Expressing Squared Numbers as Product of Two Consecutive Odd or Even Natural Numbers

It turns out that you can write almost any squared number in terms of the product of two odd or even integers plus one. As an example, let’s go through the following operation:

29 * 31 = (30 – 1)(30 + 1) = 30^2 – 1  because (a – b)(a + b) = a^2 – b^2

30^2 = 29 * 31 + 1

So as you can see here, you can write 30^2 as the product of two consecutive odd natural numbers, 29 and 31 and add 1 to the product. You can do this with almost every square number. I am using the word “almost” here since I have not taken the time to test every possible case not have I proved this nor have I seen a proof for it.

Wherever this happens to come in handy depends on the kind of problems you might be solving.