Question

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.​

Answer 1

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

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