for only mathematicians...
que no 11 or 12
plz help....
no sparm...!!
THANK U....☺
Attachments:
Answers
Answered by
4
11. Assume that√7 is rational
rational numbers are in the p/q form, where q nots equals to zero
√7=a/b, a and b are co primes
Cross multiply
√7b=a
Squqring on both sides
7b^2=a^2
Therefore b^2=a^2/ 7
So 7 divides a^2
And 7 divides a
Now assume a constant a=7c
Squaring on both sides
a^2=49c^2
We know that a^2=7b^2 so substitute in that place
Therefore, 7b^2=49c^2
Cancelation b^2=7c^2
7 divides b
7 divides b square
So a, b are not coprimes therefore our assumption is wrong
Therefore √7 is irrational
Hence proved
rational numbers are in the p/q form, where q nots equals to zero
√7=a/b, a and b are co primes
Cross multiply
√7b=a
Squqring on both sides
7b^2=a^2
Therefore b^2=a^2/ 7
So 7 divides a^2
And 7 divides a
Now assume a constant a=7c
Squaring on both sides
a^2=49c^2
We know that a^2=7b^2 so substitute in that place
Therefore, 7b^2=49c^2
Cancelation b^2=7c^2
7 divides b
7 divides b square
So a, b are not coprimes therefore our assumption is wrong
Therefore √7 is irrational
Hence proved
Similar questions