Math, asked by anmolnegi41861, 8 months ago

Prove that √7 is irrational.

b) Prove that 3 + 2√5 is irrational.

c) Prove that 3 + √2 is an irrational number.

d) Prove that 3√5 – 8 is irrational.

e) Show that

1

2 + √3

is irrational.​

Answers

Answered by anweshachetia10
9

Answer:

Step-by-step explanation:

c) To prove:  3 + \sqrt{2} is irrational

 Proof:    Let 3 + \sqrt{2} be a rational no.

  ∴ 3 + \sqrt{2} = \frac{a}{b} ( where a and b are co primes)

    \sqrt{2} = a/b - 3

    Since a and b are integers, a/b - 3 is rational, hence \sqrt{2} is rational.

  But this contradicts the fact that \sqrt{2} is irrational.

   ∴ This contradiction has arisen due to our wrong assmption that 3 + \sqrt{2} is        

       rational.

      ∴ 3 + \sqrt{2} is irrational.

        Hence proved!!!

     now you can solve question b), d) and e) in the same way

    I hope it helps you

       Thank you

    If you liked my answer please mark me as brainliest

Similar questions