CBSE Class 10 Answered

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

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 | 08 Jul, 2014, 05:11: PM

Expert Answer

$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$