Question

prove that root 3+5 is irrational

Answer 1

Answer:

let root3+5 be a rational

so, root 3+5 = a/b (a and b are co primes)

squaring both sides

(root5+3)*2 = (a/b)*2

5+3=a*2/b*2

7b*2=a*2.....(1)

7b=a

so a is a factor of 5+3

once more squaring both sides

49q*2 = 7b*2...form (1)   q = any positive integer

7q*2=b*2

7q = b

b is a factor of 7

therefore, our supposition was wrong

therefore a and b are not co primes

so root3+5 is an irrational number

may it helps you

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