Square and square roots
Square and square roots of Class 8
SQUARE NUMBERS
Roots" (or "radicals") are the "opposite" operation of applying exponents; you can "undo" a power with a radical, and a radical can "undo" a power. For instance, if you square 2, you get 4, and if you "take the square root of 4", you get 2; if you square 3, you get 9, and if you "take the square root of 9", you get 3:
The "" symbol is called the "radical"symbol. The expression "√9 " is read as "root nine", "radical nine", or "the square root of nine".
If a natural number m can be expressed as n^{2}, where n is also a natural number, then m is square number.
e.g., 22 = 2 × 2 = 4
9 = 3 × 3 = 3^{2} etc.
PERFECT SQUARES:
The numbers 1, 4, 9, 16,..... are square numbers. These numbers are also called perfect squares.
A perfect square numbers end with 0, 1, 4, 5, 6 or 9 at unit's place.
 If a number end with 2, 3, 7 or 8 at unit's place, it can never be a perfect square.
 If a number has 1 or 9 in the unit's place, then it's square ends in 1.
 When a square number ends in 6, the number whose square it is will have either 4 or 6 in unit's place.
 Squares of even numbers are always even.
 Squares of odd numbers are always odd.e.g.
question What is 3 squared?
3 Squared 
= 

= 3 × 3 = 9 
"Squared" is often written as a little 2 like this:
This says "4 Squared equals 16"(the little 2 says the number appears twice in multiplying)
SQUARES FROM 12 TO 62:
1 Squared 
= 
12 
= 
1 × 1 
= 
1 
2 Squared 
= 
22 
= 
2 × 2 
= 
4 
3 Squared 
= 
32 
= 
3 × 3 
= 
9 
4 Squared 
= 
42 
= 
4 × 4 
= 
16 
5 Squared 
= 
52 
= 
5 × 5 
= 
25 
6 Squared 
= 
62 
= 
6 × 6 
= 
36 
NEGATIVE NUMBERS:
You can also square negative numbers.
question 1. What happens when you square (5) ?
Sol. (5) × (5) = 25 (because a negative times a negative gives a positive)
When you square a negative number you get a positive result.
Just the same as if you had squared a positive number:
(For more detail read Squares and Square Roots in Algebra)
Note: if someone says "minus 5 squared" do you:
You get different answers:
Square 5, then do the minus: Square (5):
(5×5) = 25, (5)×(5) = +25
Always make it clear what you mean, and that is what the "( )" are for. NCERT solutions for class 8 Maths prepared by Physics Wallah will help you to solve your NCERT text book exercise.