RBSE Class 8 Maths Notes Chapter 6 Square and Square Roots

These comprehensive RBSE Class 8 Maths Notes Chapter 6 Square and Square Roots will give a brief overview of all the concepts.

RBSE Class 8 Maths Chapter 6 Notes Square and Square Roots

→ Square Number: If a natural number m can be expressed as n², where n is also a natural number, then m is a square number or perfect square.
Ex. 25 is the square of 5, so 25 is a perfect square or square number

→ A number ending in 2, 3, 7 or 8 is never a perfect square. In other words all square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.

→ Square numbers can only have even number of zeros at the end.
Ex. 8100 = 902 is a perfect square.

→ A perfect square (other than 1) leaves a remainder 0 or 1 when divided by 3.

→ A perfect square (other than 1), when divided by 4, leaves a remainder 0 or 1.

→ Squares of even numbers are always even.

→ Squares of odd numbers are always odd.

→ The sum of first n odd natural numbers is n².

→ Any odd number can be expressed as sum of consecutive natural number.

→ If a number has 1 or 9 in the unit’s place, then its square ends with 1.

→ When a square number ends with 6, the number whose square it ils, will have either 4 or 6 in unit’s place.

→ Between n² and (n + 1)² there are 2n numbers which is 1 less than the difference of two squares.

→ If a perfect square is of n-digits then its square root will have \(\frac{n}{2}\) digits if n is even or \(\frac{(n+1)}{2}\) if n is odd.

→ Pythagorean Triplets: A triplet m, n and p of three natural numbers is called a Pythagorean triplet, if m² + n² = p²
Ex. (7, 24, 25) is a Pythagorean triplet.
Let m = 7; n = 24; p = 25
then 7² + 24² = 25²
For any natural number where m > 1 (2m, m² - 1, m² + 1) is a Pythagorean triplet.

→ If a and b are any two whole numbers, then
\(\sqrt{a b}=\sqrt{a} \times \sqrt{b}\)
\(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\)

→ If x = a², then √x = a

→ The squares of numbers 1, 11, 111, ..... etc. They give a beautiful pattern:
1² = 1
11² = 121
111² = 12321
1111² = 1234321
11111² = 123454321
another interesting pattern
7² = 49
67² = 4489
667² = 444889
6667² = 44448889
66667² = 4444488889