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Source for some of the images in this post:
A Maths Dictionary for Kids by © Jenny Eather
1) Exponents
Basic operations of indices |
Math operations
 | Examples
|
am∗an=am+n | 73∗75=73+5=78 |
aman=am−n | 7375=73−5=2−2 |
(am)n=am∗n | (72)3=72∗3=76 |
x−n=1xn | 7−2=172 |
(ab)−n=(ba)n | (17)−2=72 |
1am=a−m | 173=7−3 |
n√am=(am)1n=amn | 3√76=(76)13=763=72=49 |
a0=1, if a≠0 | 70=1 |
(−a)even=+(a)even a>0 | (−7)4=−7×−7×−7×−7=74=2,401 |
(−a)odd=−(a)odd a>0 | −(7)3=−(7×7×7)=−343 |
Note (am)n≠amn(72)3=76However
732=79. You have to elevate
32 before and then
7976≠792) Unit Digit Power
Unit Digit or Last Digit of a^n |
a\n
 | 1
 | 2
 | 3
 | 4
 | cyclicity
 |
0 | 0 | 0 | 0 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 |
2 | 2 | 4 | 8 | 6 | 4 |
3 | 3 | 9 | 7 | 1 | 4 |
4 | 4 | 6 | 4 | 6 | 2 |
5 | 5 | 5 | 5 | 5 | 1 |
6 | 6 | 6 | 6 | 6 | 1 |
7 | 7 | 9 | 3 | 1 | 4 |
8 | 8 | 4 | 2 | 6 | 4 |
9 | 9 | 1 | 9 | 1 | 2 |
ExampleFind the unit digit of
799?
Having a cyclicity of 4 we do have that
710 has a unit digit of 9. This for nine times which is
790= unit digit of 9 + 9 spots the unit digit is
33) Unit Digit of a SquareThe square of a number can never end with 2,3,7,8 or odd number of zeros.4) Number rearrangementWhen a two-digit number is reversed then the
sum of two numbers is
always divisible by 11 & the
difference of two numbers is
always divisible by 9Let's say we have a number
92When reversed it will be
29Sum = 92+29 =
121 ----> Divisible by
11Difference = 92-29 =
63 ----> Divisible by
9 5) Square of 5Suppose that X is a number ending in 5 or 5 itself
(X5)2=X(X+1),256252=62×63,
25=390625You just need to multiply
62×63 and add
256) Square of any numbern2=(n−d)(n+d)+d2d is the distance from the
nearest multiple of
10.100192=(19−1)(19+1)+12=18×20+1=3612) Roots1) Properties of radicals
2) Surds• another name for an irrational number.
• a surd is a real number that can be written as a nonrepeating or nonterminating decimal but not as a fraction because the decimal goes on forever without repeating.

source:
http://www.amathsdictionaryforkids.com/Surds are irrational roots of a rational number. e.g. √6 = a surd ⇒ it can’t be exactly found. Similarly – √7, √8,
3√9,
4√27 etc. are all surds.
- Pure Surd : The surds which are made up of only an irrational number e.g. √6, √7, √8 etc.
- Mixed Surd : Surds which are made up of partly rational and partly irrational numbers e.g. 3√3, 64√27 etc.
- Rationalization of Surds: In order to rationalize a given surd, multiply and divide by the conjugate of denominator [conjugate of (a + √b) is (a – √b) and vice versa].
e.g.
(6+√2)(1−√3)=(6+√2)(1+√3)(1−√3)(1+√3)=(6+6√3+√2+√6)(1−3)=(6+6√3+√2+√6)−2Attachment:
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