MATHS SYMBOLS - ROOTS - SQUARES and SQUARE ROOTS - DEFINITIONS - ROOTS and THEIR PROPERTIES - 10+ PROPERTIES - RATIONALISING the DENOMINATOR - RADICAL EQUATION - PROOFS, EXAMPLES - CALCULATIONS STEP by STEP www.enzoexposito.it/mobile/matematica.html www.enzoexposito.it/mobile/aritmetica.html

1. ENZO EXPOSYTO
MATHS
SYMBOLS
ROOTS and THEIR PROPERTIES
Enzo Exposyto 1

2. 2√16 2√9 2√4 2√1 2√0
ROOTS
3√-27 3√-8 3√-1 3√0
Enzo Exposyto 2

3.
Enzo Exposyto 3

4. 1 - Squares and Square Roots 6
2 - Definitions 10
3 - Roots and Their Properties 20
4 - Property 0 22
5 - Property 1 25
6 - Property 2 31
7 - Property 3 34
8 - Property 4 38
9 - Property 5 42
Enzo Exposyto 4

5. 10 - Property 6 46
11 - Property 7 51
12 - Property 8 55
13 - Property 9 - Rationalising the Denominator 63
14 - Equation 76
15 - SitoGraphy 78
Enzo Exposyto 5

6. SQUARES
and
SQUARE ROOTS
Enzo Exposyto 6

7. SQUARES and SQUARE ROOTS
3 squared = 32 = 3 × 3 = 9
The SQUARE ROOT
2√9
GOES the OTHER WAY:
32
2√9
Enzo Exposyto 7

8. The SQUARE ROOT of 9 is 3
2√9 = 3
BECAUSE
3 squared is 9;
so
the square root of 9
is 3:
32
2√9
Enzo Exposyto 8

9. THE SQUARE ROOT 2√9
COMES BACK
TO THE BASE 3
SQUARE ROOT SQUARE
1 1
2 4
3 9
4 16
Enzo Exposyto 9

10. DEFINITIONS
Enzo Exposyto 10

11. the special SYMBOL
that means
"nth root"
with integer n > 0
Enzo Exposyto 11

12. DEFINITION
1)
GENERALLY speaking,
iff
(if and only if)
bn = a
Enzo Exposyto 12

13. DEFINITION
1)
Example:
because 23 = 8;
Example:
3√(-8) = -2
because (-2)3 = -8
Enzo Exposyto 13

14. DEFINITION
1)
Example:
2√(-1) = ?
HAS NO SOLUTION
because
DOES NOT EXIST
such that
x2 = -1
Enzo Exposyto 14

15. DEFINITION
2)
IF n IS ODD
then
Example:
Enzo Exposyto 15

16. DEFINITION
3)
IF n IS EVEN
then
Example:
Enzo Exposyto 16

17. DEFINITION
4)
IF a ≥ 0 THEN
Examples:
and
Enzo Exposyto 17

18. DEFINITION
BRIEFLY,
means a = bn
where
a and b are real numbers IF n IS ODD
and
a ≥ 0 and b ≥ 0 IF n IS EVEN
Enzo Exposyto 18

19. ROOTS TABLE
a n > 0
n is ODD n is EVEN
a < 0
a ≥ 0
Enzo Exposyto 19