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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:

Square and square

The "Square and square" 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

=

powers-square

= 3 × 3 = 9

  "Squared" is often written as a little 2 like this:

Square and square

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. 

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