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.
Squares and Square Roots Sample Questions for Class 8
Question 1
Find the smallest number to be multiplied to make 1746 a perfect square.
A. 9
B. 2
C. 97
D. 194
Question 2
There are 5800 students to be arranged in rows and columns.
Number of rows and columns are equal.
How many children are in each row ?
How many children are left out ?
A. 77,23
B. 88,20
C. 76,24
D. 80,13
Question 3
Find pythagorean triplet of 32.
A. 32, 255 , 257
B. 15, 16 , 17
C. 32, 33,34
D. 254, 255,257
Question 4
Which of the following smallest square number divisible by 2,3 and 6?
A. 576
B. 3600
C. 900
D. 324
Question 5
Raghav bought 20kg of wheat at ₹32 per kg.
The price was reduced by 10% per kg next month.
How much more wheat can he buy with same amount?
A. 2.2 kg
B. 4 kg
C. 3.6 kg
D. 1.7 kg