prove that root 7 is a irrational number
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Let root7 be rational.
We know that every rational is expressed in the form p/q where p and q r co primes and q is not equal to 0
So, √7 =p/q
(√7)^2=(p/q)^2
7=p^2/q^2
7/p^2=q^2
7/q^2
7/q
Now, q=7r for some integer r
q^2=49r^2
7p^2=49r^2
p^2=7r^2
7/p^2
7/√7 p
From above , it contradicts that p and q are co primes . so our assumption is wrong.
Hench √7 is irrational.
Hope it helps....
We know that every rational is expressed in the form p/q where p and q r co primes and q is not equal to 0
So, √7 =p/q
(√7)^2=(p/q)^2
7=p^2/q^2
7/p^2=q^2
7/q^2
7/q
Now, q=7r for some integer r
q^2=49r^2
7p^2=49r^2
p^2=7r^2
7/p^2
7/√7 p
From above , it contradicts that p and q are co primes . so our assumption is wrong.
Hench √7 is irrational.
Hope it helps....
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