Question

prove that root2+root7 is an irrational ​

Answer 1

let us assume that root2 is rational and it is in the form of a and b where a and b are co-primes(the both a and b have no other factor than one)

so

root2=a/b

squaring both side

(root2)2 = (a/b)2

2 = a2/b2

Take b2 to LHS

2 b2= a2

according to theorem 1.3 if 2 divides a2 then 2 divides a

let a = 2c

2 b2 = (2c)2

b2 = 2c2

it means that 2 divides b2 therefore 2 divides b

so from above we can know that a and b have 2 as an other factor than 1.so our supposition was wrong

therefore root 2 is irrational

similarly root7 can be proven irrational
HOPE IT HELPS

Answer 2

Hi mate

it is attached

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