What is a Square Number?
According to the square number definition, they are the numbers that are multiplied by themselves. In other words, if a natural number is multiplied by itself, it is known as a square number. For example, 2 multiplied by itself (2x2) is a square number. When we multiply two equal integers by each other, the result of that ticket is basically a perfect square. Square numbers cannot be negative because if a negative number is multiplied by the same negative number it results in a positive number. Hence, square numbers are always positive.
Square numbers are named after a square because they form an area of a square. Imagine you have 9 items of 3 different categories. If we arrange it into a grid of 3 columns and 3 rows (3*3=9) placed vertically and horizontally, the grid will form a square.
Squaring Decimals
Just like squaring whole numbers (integers) is easy, it is also very easy to square decimals and both are done in the same way.
For example, 1.53 x 1.53 = 2.3409
7.19 x 7.19 = 51.6961
Properties of Square Number
Property 1- Square numbers will always end with the digits 0,1,4,5,6 and 9. For example 9,14,25,81,100 are perfect squares whereas numbers like 17,22,83 are not perfect numbers.
Property 2- A square number always contains an even number of zeros at the end and numbers containing an odd number of zeros cannot be square numbers. For example, 1600 3600 2500 square numbers whereas 1000, 250,160 are not square numbers.
Property 3- A number containing 1 or 9 as the last digit will always have 1 at the end of its square number. For example, the square number of 9 is 81 and 11 is 121.
Property 4- A number that has 4 or 6 as the last digit will have a square number ending with 6. For example, the square root of 4 is 16 and the square of 16 is 256.
Property 5- The square of an odd number is always odd and the square of an even number is always the reason. For example, the square of 15 is 125 and the square of 22 is 484.
Property 6- Square numbers a positive as two negative signs multiplied by each other result in a positive sign. For example -5×-5=25.
Property 7- Square root of a square number is a whole number. For example, the square root of 441 is 21 so your 441 is a square number. If the square of a number is a decimal of a fraction number then the number is not a perfect square. For example, √56=7.48, so your 56 is not a perfect square.
Property 8- For every natural number n, (n+1)²-n²=(n+1)+n.
Property 9- The sum of first n odd natural numbers is equal to the square of a number n.
1²=1
2²=1+3
3²=1+3+5
4²=1+3+5+7 and so on.
Property 10- For any natural number M greater than 1,
(2m,m²-1,m²+1) is a Pythagorean triplet.
Below is the Table of Square Numbers From 1 to 100:
FAQs on Square Numbers
1. What is the relation between square numbers and square root?
When a square root is multiplied, it produces a square number. Thus, a square root has an inverse operation than the square number. Let’s take an example, the square root of 36 is 6 because 6 x 6 = 36. So, we can say 36 is a square number and 6 is the square root of it. Finding the square root of a number can be much trickier than calculating the square number. Therefore, the modern calculator has the square root button to make the calculation easier.
2. How do we Square Negative Numbers?
We all know that when two negative or two positive numbers are multiplied to each other then the result will always be a positive number. For example, if we multiple -5 to -5 then the result will be 10. If 5 will be multiplied to 5, the result will be 10 as well. But what if a negative number is multiplied to a positive number or vice versa? The result would be a negative number. For example, if -3 is multiplied to 3, the result would be -9. A number cannot be a square number if it is a negative number because -3 and 3 are very different from each other.
3. What is the symbol of a square number?
A square number can be denoted as n×n. For instance, the product derived by multiplying 2 is 4, so here, 4 is termed as a perfect square. Exponential notation is a square number donated as n² and is pronounced as "n" squared. For example 20×20=400, 21×21=441, 22×22=484.
4. How can you tell if a number is a perfect square?
There are a lot of ways to determine whether a number is a perfect square. By using repeated division by prime factors we can find out whether a number is a perfect square or not. For example, to check whether 441 is a perfect square, you can start by factoring this number like 441=3×3×7×7. Here we can see that 3 and 7 are the numbers that exist twice. Make two sets 3×7×3×7 and multiply them 3×7=21 and 3×7=21. We get 21 twice that can also be written as 21². So we can conclude that 441 is a perfect square.
5. Who invented square numbers?
Around 1650 BC, the Egyptians used an inverse proportion method to calculate square roots. Somewhere around 200 BC, Chinese mathematical writings demonstrate that the square numbers were approximated by using the deficiency and excess method. Regiomontanus was the one who invented a symbol written as R for square roots.
6. What is the square root of 0?
The square root of 0 is equal to the square root of 0². It has only one square root and in fact, 0 is the only real number. The square root of 0 is itself 0. A square number is the product of a number that gets multiplied by itself. If we multiply 0 twice by itself 0×0= then the answer will be 0, itself.