is √7 a rational no. or irrational no. with proof
Answers
Answer:
√7 is a irrational number...
because every prime number which is urder root is irrational number....it means it can't be written as p/q form...
hope it helps....
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Solution:-
==> √7 is irrational number.
Proof:-
==> Lets assume that √7 is rational number. ie √7=p/q.suppose p/q have common factor thenwe divide by the common factor to get √7 = a/b were a and b are co-prime number.that is a and b have no common factor.
==> √7 =a/b co- prime number
==> √7= a/b
==> a=√7b
==>squaring both the sides..
==> a²=7b² .......(1)
==> a² is divisible by 7
==> a=7c
==> substituting values in 1
==> (7c)²=7b²
==> 49c²=7b²
==> 7c²=b²
==> b²=7c²
==> b² is divisible by 7 that is a and b have atleast one common factor 7.
is a and b have atleast one common factor 7.
==> This is contridite to the fact that a and b have no common factor.
==> This is happen because of our wrong assumption √7 is irrational.
