Question

how to prove 7 root 3 is irrational number how to prove 7 root 3 is irrational number ​

Answer 1

Answer:

∴a and b has common factor as 147. But our assumption is HCF(a,b) = 1. ∴Our assumption is wrong. Hence, 7√3 is an irrational no.

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Answer 2

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....