Square roots of non-perfect squares

We can write the number 40 as 2 × 2 × 2 × 5. This is not a perfect square because we cannot pair the factors.

We write \(\sqrt{40}\) to be the square root of 40, and can investigate between which two whole numbers it lies.

Consider the table of perfect squares below:

Whole number	1	2	3	4	5	6	7	8	9	10	11	12
Whole number squared	1	4	9	16	25	36	49	64	81	100	121	144

The number 40 lies between 36 and 49 hence \(\sqrt{40}\) lies between 6 and 7.

Similarly, 12 lies between 9 and 16 so \(\sqrt{12}\) lies between 3 and 4.

These numbers can be shown approximately on the number line.

Detailed description