Question

Given that root 2 is irrational. Show that 5 + root 2 is irrational.

Answer 1

Answer:

Given: root2 is irrational

Now,let us assume that 5 + root2 is rational

So,

5+root2 = a/b

root2 = a/b-5

Root2 = a-5b/b

This means root 2 is rational.

But we know that root2 is irrational.

So, our assumption was wrong.

Hence, 5+root2 is irrational.

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Answer 2

Step-by-step explanation:

let us assume that 5+$\sqrt{2}$ is a rational number

5+$\sqrt{2}$ =p/q

$\sqrt{2}$ =p/q-5 (rational-rational=rational)

therefore p/q-5 is rational then $\sqrt{2}$ is also rational

but it is given that $\sqrt{2}$ is irrational in the question

so, it is contradiction to our assumption

then  5+$\sqrt{2}$ is irrational.

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