Square roots

Study the following situations.

(a) Area of a square is 144 cm2. What could be the side of the square ?

We know that the area of a square = side2.

If we assume the length of the side to be ‘a’, then = a2.

To find the length of side it is necessary to find a number whose square is 144.

(b) What is the length of a diagonal of a square of side 8 cm ?

Can we use Pythagoras theorem to solve this ? We have:

AB2+BC2=AC2

82+82=AC2

+ = AC2

= AC2

Again to get AC, we need to think of a number whose square is 128.

(c) In a right triangle, the length of the hypotenuse and a side are respectively, 5 cm and 3 cm. Can you find the third side ?

Using Pythagoras theorem 52 = x2+32

– = x2

= x2

Again, to find 'x' we need a number whose square is 16.

In all the above cases, we need to find a number whose square is known. Finding the number with the known square is known as finding the square root.

Finding square roots

The inverse (opposite) operation of addition is and the inverse operation of multiplication is .

Similarly, finding the square root is the inverse operation of squaring a number.

We have:

12 = 1, therefore square root of 1 is

22 = 4, therefore square root of 4 is

32 = 9, therefore square root of 9 is

Instructions

Instructions

From the above, you may say that there are two integral square roots of a perfect square number. In this chapter, we shall take up only positive square root of a natural number.

Positive square root of a number is denoted by the symbol ·.

For example: 4 = 2 (not –2);9 = 3 (not –3) etc.