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 n2, where n is also a natural number, then m is square number.
e.g., 22 = 2 × 2 = 4
9 = 3 × 3 = 32 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.
