Question

plz tell me how i do my sum tommorrow is my exam plz 1 ques

Answer 1

Hello

let root 5 be rational
then it must in the form of p/q [q is not equal to 0][p and q are co-prime]
root 5=p/q
=> root 5 * q = p
squaring on both sides
=> 5*q*q = p*p ------> 1
p*p is divisible by 5
p is divisible by 5
p = 5c [c is a positive integer] [squaring on both sides ]
p*p = 25c*c --------- > 2
sub p*p in 1
5*q*q = 25*c*c
q*q = 5*c*c
=> q is divisble by 5
thus q and p have a common factor 5
there is a contradiction
as our assumsion p &q are co prime but it has a common factor
so √5 is an irrational

Answer 2

HERE ARE THE SOME SIMPLE STEPS THAT CAN HELP U IN SOLVING THIS FIRST QUESTION
FIRST U HAVE TO START LIKE THIS
=> LET US ASSUME ON THE CONTRARY THAT ROOT5 US RATIONAL NUMBER. THEN THERE EXISTS CO PRIME POSITIVE INTEGERS A AND B SUCH THAT
ROOT5 = A/B(A,B ARE CO PRIME INTEGERS AND B=×0)
=>TAKING B TO ANOTHER SIDE
AND SQUARING BOTH SIDE
WE GET 5B SQUARE = A SQAURE
IT BECOMES 5BSQUARE = A SQUARE
OR A SQUARE = 5B SQUARE ((1))
=> 5 IS A FACTOR OF A SQUARE, => 5 IS A FACTOR OF A .
LET A=5C ( C SOME INTEGER)
=> SQUARING BOTH SIDES
A SQUARE = 25C SQUARE
=> FROM EQUTION ((1))
=>5B SQUARE = 25C SQUARE
=> B SQUARE = 25C SQUARE/ 5 (CANCLE OUT BY 5)IT BECOME
B SQUARE = 5C SQUARE
=> 5 IS A FACTOR OF B SQUARE => 5 IS A FACTOR OF B.
THEREFOR 5 IS A COMMON FACTOR OF A,B.
BUT THIS CONTRADICTS THE FACT THAT A,B ARE CO PRIMES.
THEREFOR ROOT 5 IS IRRATIONAL NUMBER ☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺HOPE THIS WILL HELPS U IN YOUR EXAM AND ONE ADVICE I WANT TO GIVE THAT IF U CAN'T REMEMBER THEN PRATICE MANY TIMES AND I ADVICE THAT LEARN IT..BECAUSE IT ÂŁWÄÝŚ COME IN EVERY EXAM AND CAN GIVE U 3 OR MORE THAN 3 .HOPE U UNDERSTAND....