#### notes

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 = `"side"^2`

If we assume the length of the side to be ‘a’, then `144 = a^2`

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

(b) In a right triangle the length of the hypotenuse and a side are respectively 5 cm and 3 cm in fig.

Let x cm be the length of the third side.

Using Pythagoras theorem,

`5^2 = x^2 + 3^2`

25 – 9 = `x^2`

16 = `x^2`

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

Finding the number with the known square is known as finding the square root.

**Finding square roots :**

The inverse (opposite) operation of addition is subtraction and the inverse operation of multiplication is division. Similarly, finding the square root is the inverse operation of squaring.

We have, `1^2` = 1, therefore square root of 1 is 1

`2^2` = 4, therefore square root of 4 is 2

`3^2` = 9, therefore square root of 9 is 3 .