Question

prove that 5-3 root 7 is an irrational​

Answer 1

Step-by-step explanation:

Let 5-3√7be rational

i. e., 5-3√7=a/b (where a and b are co-primes )

now, 5-3√7=a/b

-3√7=a/b–7

√7=(7b–a) /3b

now, we know that under root 7 is a a irrational number but our answer contradicts this fact so our assumption that 5 - 3 under root 7 is rational is is wrong thus 5 - 3 under root 7 is is irrational

Answer 2

let, it is an rational number

then it is written in the form of p/q where p and q are integer and it has no any common factor

5-3√7

5-3√7=p/q

squaring on both side

$(5 - 3 \sqrt{7} ) ^{2} = p ^{2} \div q ^{2}$

25+63-30√7= p^2/q^2

88-30√7 =p^2/q^2

30√7=p^2/q^2-88

30√7=p^2-88q^2\q^2