Learn Class 8 Math - Squares and Square Roots

Introduction to Square Numbers

A natural number m with the formula n/2 is a square number if n is also a natural number.

Example: 1, 4, 9, 16, and 25.

Calculating the square of a number

If n is a number, then its square can be expressed as n * n = n square

E.g. The square of six is equal to 6*6 = 36

Using identity to find the square of a number

You can easily find the squares of numbers with two or more digits by summing two numbers.

For example: 23 square = (20 + 3) 2 = 20 (20+3)+3(20+3) = 20 square+20×3 + 20×3 + 32 = 400 + 60 + 60 + 9 = 529

Properties of the Square Number:

• There's no perfect square if the number ends in 2, 3, 7, or 8.
• Zeros on an odd digit don't make a perfect square.
• Even numbers squared equal an even number.
• When a number is odd, its square is odd.
• Squares of proper fractions are smaller than their fractional parts.
• Each natural number n has the formula [(n + 1)2 - n2} = {(n + 1) + n}.
• Natural number n 2 = sum of first n odd numbers.
• The triplet consisting of m, n, p is called a Pythagorean triplet if (m2 + n2) = p2.
• The Pythagorean triplet is formed by (2m, m2 – 1, m2 + 1) for every natural number m > 1.