Squares And Square Roots


By square of a number, we mean a number multiplied by itself. The product that we get on multiplying a number by itself is called the square of the number. Let us take a number ‘a’, its square is given by a * a & is denoted by a2. A simple example of square of a number is what we have learnt in lower classes as the formula to find the area of a square gives the length of the side of the square. Area of a square is given as: Area = side * side. In other words, we can say that the area of a square is the square of the length of its side or Area = (side) 2. If a number is a square of a natural number, it is called a perfect square; else it is a non-perfect square. For example: 12 * 12 = 144. Here, 144 is called the perfect square of 12.

We will learn about square and square roots here.

As learnt in earlier classes, addition & subtraction are opposite operations; also multiplication & division are opposite operations in mathematics. Similarly, Squares and square roots are also opposite terms. If a number is the square of second number, then second number is said to be the square root of the first number. In (12) 2 = 144, 144 is the square of 12 & also, 12 is the square root of 144.

The square root of a number, ‘a’ is given by (a) ½ .

To find square and square root, we should remember that square is the product of a number with itself, while in square root, we first find the prime factors of the given number & then pair the same factors, example; we first find the prime factors of 144, we get 144= 2*2*2*2*3*3.

So,now, pairing the same prime factors & removing the square root sign taking the prime factors only once. 

There are some properties of perfect squares that make our task easier. These are:

*A perfect square never has 2, 3, 7 or 8 at its ones place.

* A perfect square never has an odd number of zeros at its end.

*The square of an even number is always even.

*The square of an odd number is always odd.

*Two consecutive square numbers, n& (n + 1) 2, have 2n non-perfect square numbers between them.

Math Topics