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Irrational Numbers

Prove that 4-...

Question

Prove that $4 - 5 \sqrt{2}$ is an irrational number.

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Solution

Let us assume that is rational .Then, there exist positive co primes a and b such that

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Q. Prove that (

4 - 5 \sqrt{2}

) is an irrational number.

(3 + 5 \sqrt{2})

is an irrational number, given that

\sqrt{2}

is an irrational number.

(4 - \sqrt{3})

is an irrational number, given that

\sqrt{3}

is an irrational number.

4 - \sqrt{3}

is an irrational number.

(2 \sqrt{3} + \sqrt{5})

is an irrational number. Also check whether

(2 \sqrt{3} + \sqrt{5}) (2 \sqrt{3} - \sqrt{5})

is rational or irrational

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