Sub. :- Mathematics

Squares and Square Roots

Std. :- 6th

Chapter no. 9

How to Square A Number

Any number multiplied by itself is called square of that number.

3 Squared = = 3 × 3 = 9

Example: What is 3 squared?

"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)

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

Write the squares of the following numbers

1)102)63)124)1105)806)200

Answers :-

1) 102 = 10 X 10 =100

2) 62 = 6 X 6 =36

3) 122 = 12 X 12 = 144

Write the squares

1) 322

2) 202

3) 1332

Square of any number having 5 in unit place

Let us take an example 252 = (2× (2+1)) │ 52

= (2× 3) │25 = 625So 252 = 625

Let us take one more example 452 = (4× (4+1)) │ 52

=4× 5 │25452 =2025

Practice:1) 352

2) 552

3) 952

4)1052

5)1152

Negative Numbers

You can also square negative numbers.

Example: What happens when you square (-5) ?Answer:

(-5) × (-5) = 25 (because a negative times a negative gives a positive)

That was interesting!When you square a negative number you get a positive result. Just the same as if you had squared a positive number:

Square 5, then do the minus: Square (-5):

-(5×5) = -25 (-5)×(-5) = +25

Note: if someone says "minus 5 squared" do you:•Square the 5, then do the minus? •Or do you square (-5) ?

You get different answers:

Finding the square root of a number is the inverse operation of squaring that number. Remember, the square of a number is that

number times itself.

The Square root

The perfect squares are the squares of the whole numbers.

This is the symbol of square root

The square root of a number, n, written below is the number that gives n when multiplied by itself.

The square root of a number, n, written

is the number that gives n when multiplied by itself. For example,

because 10 x 10 = 100

ExamplesHere are the square roots of all the perfect squares from 1 to 100.