Squares and square

Q1

What are squares and square roots?

Square numbers are the numbers which are produced when a value is multiplied by itself. Say if n is a number and is multiplied by itself, then the square of n is given by n². For example, the square of 10 is 10² = 10 x 10 = 100.

The square root of a number is a value which on multiplied by itself gives the original number. It is represented by the symbol ‘√’. For example, the square root of 25 is √25 = 5.

Q2

What are perfect squares? Give an example

Perfect squares are the numbers, the square root of which gives a whole number. For example, 9 is a perfect square, because its root is a whole number, i.e.√9 = 3.

Q3

What is an imperfect square with examples?

An imperfect square is a number, the square root of which gives a fraction. The value generated by taking the square root of the imperfect square could be non-terminating as well.

For example, 3 is an imperfect square, because its root is equal to,

√3 = 1.73205080757, which is a fraction.

Q4

How to find the square root?

To find the square root of a number we can use the prime factorisation method. For example, the square root of 900 is:

√900 = √(2 x 2 x 3 x 3 x 5 x 5 )

Taking out the numbers in pairs, we get;

√900 = 2 x 3 x 5 = 30

900 was a perfect square, but to find the root of an imperfect square, we have to use long division method.

Q5

What is the difference between a square and square roots?

The square root of a number gives the root of a number which was squared. This is the primary difference between them.