Perfect SquaresDefinitionsIn mathematics, a perfect square or square number is a positive integer that is square of an integer. In other words, when we multiply two same numbers together, then the product that we get is called the perfect square. In short, it is the product of two positive equal integers or product of an integer with itself. Notation of Perfect SquareThe perfect square is denoted by x^{2} (pronounced as squared) where x is called the base, and 2 is called the power. It means multiply two times, i.e., x×x. For example, when we multiply 5 by 5, we get 25 as the result. It is called the perfect square. Perfect Squares Table
We can conclude from the above table that the perfect square of a number can be calculated by adding the previous number, current number (for which calculating the square), and the square of the previous number. Suppose, we want to find the square x, then:
x^{2}= (x1)^{2}+(x1)+x
Square of a Negative NumberWe can also find the square of negative numbers. But remember that:
()×()=+
It means the square of a negative number is always a positive number. For example, the square of 7^{2} is 49. Square of a Decimal NumberWe can also find the square of a decimal number. To achieve the same, ignore the decimal for a moment and write the square of the number. After that, count the decimal digits in the number from the right. In the result, count the same number of digits from the right and put a decimal point there. For example, a square of 2.5 is 6.25. Similarly, a square of 1.1 is 1.21. Square of The FractionTo find the square of the fraction is easy. In this, we find the square of the numerator and the denominator, separately and simplify the fraction if necessary. For example, the square ofis. Square of an Irrational NumberThe number that cannot be expressed by an integer is called an irrational number. The example of irrational numbers is √7,√3, etc. The square of an irrational number is the number itself without the root sign. For example, the square of √2 is 2. Similarly, the square of √15 is 15. Properties of Square
In base 10, the square has 0, 1, 4, 5, 6 at unit places.
In base 12 and prime numbers, the square of a number always ends with square digits (0, 1, 4, 9).
Some other properties are:
(2x)^{2}=4x^{2}
(2x+1)^{2}=4(x^{2}+x)+1
Next TopicNatural Numbers

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