2.1 Squares, Square Roots, Cube and Cube Roots


2.1 Squares, Square Roots, Cube and Cube Roots
 
(A) Squares
The square of a number is the answer you get when you multiply a number by itself.

Example:
(a) 13= 13 × 13 = 169
(b)   (–10)= (–10) × (–10) = 100
(c) (0.4)2 = 0.4 × 0.4 = 0.16
(d)   (–0.06)= (–0.06) × (–0.06) = 0.0036
(e) ( 3 1 2 ) 2 = ( 7 2 ) 2 = 7 2 × 7 2 = 49 4 ( f ) ( 1 2 7 ) 2 = ( 9 7 ) 2 = ( 9 7 ) × ( 9 7 ) = 81 49


(B) Perfect Squares
1. Perfect squares are the squares of whole numbers.
 
2. Perfect squares are formed by multiplying a whole number by itself.
Example:
4 = 2 × 2   9 = 3 × 3   16 = 4 × 4
 
3. The first twelve perfect squares are:
= 12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112, 122
= 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144


(C) Square Roots
1. The square root of a positive number is a number multiplied by itself whose product is equal to the given number.
 
Example:
(a) 169 = 13 × 13 = 13 (b) 25 64 = 5 × 5 8 × 8 = 5 8 (c) 72 98 = 72 36 98 49 = 6 × 6 7 × 7 = 6 7 (d) 3 1 16 = 49 16 = 7 4 = 1 3 4 (e) 1.44 = 1 44 11 100 25 = 36 25 = 6 5 = 1 1 5


(D) Cubes
1. The cube of a number is obtained when that number is multiplied by itself twice.
Example:
The cube of 3 is written as
33 = 3 × 3 × 3
   = 27

2. 
The cube of a negative number is negative.
Example:
(–2)3 = (–2) × (–2) × (–2)
= –8
3. The cube of zero is zero. The cube of one is one, 13 = 1.


(E) Cube Roots
1. The cube root of a number is a number which, when multiplied by itself twice, produces the particular number. " 3 "  is the symbol for cube root.
Example:
64 3 = 4 × 4 × 4 3 = 4  
64 3 is read as ‘cube root of sixty-four’.

2. 
The cube root of a positive number is positive.
Example:
125 3 = 5 × 5 × 5 3 = 5

3. 
The cube root of a negative number is negative.
Example:
125 3 = ( 5 ) × ( 5 ) × ( 5 ) 3 = 5

4. 
To determine the cube roots of fractions, the fractions should be simplified to numerators and denominators that are cubes of integers.
Example:
16 250 3 = 16 8 250 125 3 = 8 125 3 = 2 5

One Comment to “2.1 Squares, Square Roots, Cube and Cube Roots”

  1. tq for this complete notes………
    i can read clearly and can understand this notes…….
    it’s very help to me tq again

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