On this page, you will find Squares and Square Roots Class 8 Notes Maths Chapter 6 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 6 Squares and Square Roots will seemingly help them to revise the important concepts in less time.

## CBSE Class 8 Maths Chapter 6 Notes Squares and Square Roots

### Squares and Square Roots Class 8 Notes Conceptual Facts

1. If a number is multiplied by itself, the product that we get is called the square of the number.

For example:

4 x 4 = 4^{2} = 16 (16 is square of 4)

20 x 20 = 20^{2} = 400 (400 is square of 20)

\(\frac{3}{5} \times \frac{3}{5}=\left(\frac{3}{5}\right)^{2}=\frac{9}{25}\) \(\left(\frac{9}{25} \text { is square of } \frac{3}{5}\right)\)

2. Square of a number is represented as the number raised to the power 2.

3. A perfect square is a number that can be expressed as the product of two equal integers.

For example: 1, 4, 9, 16, 25, …, are all perfect square numbers.

4. Properties of square numbers:

(i) No square number ends with the digits 2, 3, 7 or 8 at its unit places.

(ii) The square numbers must end with the digits 0, 1, 4, 5, 6, 9 but the number ending with 0, 1, 4, 5, 6, 9 may or may not be a perfect number.

For example: 36 is a perfect square but 56 is not.

256 is a perfect square but 346 is not.

(iii) Square of even number is always an even and the square of odd number is odd.

For example:

4^{2} = 16(even)

5^{2} = 25(odd)

(iv) A perfect square can never be a negative number.

(v) For every natural number n, (n + 1)^{2} – n^{2} – (n + 1) + n

For example: 14^{2} -13^{2} = (13 + 1) + 13 = 14 + 13 = 27

26^{2} – 25^{2} = (25 + 1) + 25 = 26 + 25 = 51

5. Pythagorean Tripletr: A triplet (m, n,p) is called a Pythagorean triplet if m^{2} + n^{2} = p^{2
}For example: (3, 4, 5), (8, 15, 17) and (20, 21, 29)

Product of two consecutive even or odd natural numbers:

Example:

11 x 13 = 143 – 12^{2} – 1 (product of odds)

13 x 15 = 195 = 14^{2} – 1 (product of odds)

44 x 46 = 2024 = 45^{2} – 1 (product of evens)

Some Patterns in square numbers: