Please give an elaborate,quick and easy answer to these questions....
 
1.How to identify whether a number is prime or composite?
2.How to add two root numbers?
3.Please show how to add   q u e s t i o n 1 right parenthesis space square root of 2 plus square root of 2 space end root end root q u e s t i o n 2 right parenthesis space square root of 3 plus square root of 9 plus square root of 25 plus square root of 27 end root end root end root q u e s t i o n space 3 right parenthesis 3 root of 3 plus 4 root of 3 q u e s t i o n space 4 right parenthesis 3 root of 7 plus 9 root of 8 q u e s t i o n space 5 right parenthesis 5 root of 175 plus 7 root of 245
 
 
4.How to know whether to use H.C.F or L.C.M in a question? Please explain very clearly.

Asked by Anishma Joseph | 8th Jul, 2014, 05:11: PM

Expert Answer:

1. F i r s t space w e space n e e d space t o space w r i t e space t h e space p r i m e space f a c t o r i z a t i o n space o f space a space g i v e n space n u m b e r. I f space t h e space f a c t o r s space o f space t h e space g i v e n space n u m b e r space a r e space 1 space a n d space t h e space n u m b e r space i t s e l f comma space t h e n space t h e space g i v e n space n u m b e r space i s space a space p r i m e space n u m b e r. I f space t h e space f a c t o r s space o f space t h e space g i v e n space n u m b e r space a r e space o t h e r space t h a n space 1 space a n d space t h e space n u m b e r space i t s e l f space left parenthesis a p a r t space f r o m space h a v i n g space 1 space a n d space t h e n u m b e r space i t s e l f right parenthesis comma space t h e n space t h e space n u m b e r space i s space a space c o m p o s i t e space n u m b e r. E x a m p l e space o f space p r i m e space n u m b e r s : space 2 comma 3 comma 5 comma 7 comma 11 comma 13 comma 17 comma 19 comma...... E x a m p l e space o f space c o m p o s i t e space n u m b e r s : space 4 comma 6 comma 8 comma 9 comma 10 comma 12 comma 14 comma 15 comma 16 comma 18 comma 20 comma..... N o w space c o n s i d e r space t h e space p r i m e space f a c t o r i z a t i o n space o f space 13 : 13 equals 13 cross times 1 T h u s comma space i t space i s space a space p r i m e space n u m b e r L e t space u s space c o n s i d e r space t h e space p r i m e space f a c t o r i z a t i o n space o f space 20 : 20 equals 1 cross times 2 cross times 2 cross times 5 T h u s comma space 20 space i s space h a v i n g space f a c t o r s space 2 space a n d space 5 space a p a r t space f r o m 1 space a n d space 20 space a n d space h e n c e space i t space i s space a space c o m p o s i t e space n u m b e r.

3. q 1 : space h o w space t o space a d d space square root of 2 plus square root of 2 end root ? L e t space u s space c o n s i d e r x plus y square root of 2 equals square root of 2 plus square root of 2 end root.... left parenthesis 1 right parenthesis w h e r e space x space a n d space y space a r e space r e a l space n u m b e r s. S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a v e open parentheses x plus y square root of 2 close parentheses squared equals open parentheses square root of 2 plus square root of 2 end root close parentheses squared rightwards double arrow open parentheses x plus y square root of 2 close parentheses squared equals 2 plus square root of 2 rightwards double arrow x squared plus 2 y squared plus 2 square root of 2 y equals 2 plus square root of 2 N o w space c o m p a r i n g space t h e space c o e f f i c i e n t s comma space w e space h a v e x squared plus 2 y squared equals 2 space.... left parenthesis 2 right parenthesis a n d space 2 square root of 2 y equals square root of 2.... left parenthesis 3 right parenthesis F r o m space left parenthesis 3 right parenthesis space w e space h a v e y equals 1 half S u b s t i t u t i n g space t h i s space v a l u e space o f space y space i n space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e x squared plus 2 open parentheses 1 half close parentheses squared equals 2 rightwards double arrow x squared plus 2 open parentheses 1 fourth close parentheses equals 2 rightwards double arrow x squared plus open parentheses 1 half close parentheses equals 2 rightwards double arrow x squared equals 2 minus open parentheses 1 half close parentheses rightwards double arrow x squared equals 3 over 2 rightwards double arrow x equals plus-or-minus square root of 3 over 2 end root T h u s comma space s u b s t i t u t i n g space t h e space v a l u e s space o f space x space a n d space y space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis space space w e space h a v e comma space square root of 2 plus square root of 2 end root equals plus-or-minus square root of 3 over 2 end root plus 1 half cross times square root of 2 rightwards double arrow space square root of 2 plus square root of 2 end root equals plus-or-minus square root of 3 over 2 end root plus fraction numerator 1 over denominator square root of 2 end fraction space space space space space space

Kindly post single question in a query and do not post multiple queries.

Answered by Vimala Ramamurthy | 9th Jul, 2014, 09:12: AM