Question

Prove that 2√3+ 5√2 is an irratinal number.​

Answer 1

Answer:-

Let 2$\sqrt{3\\}$=a/b that it is rational

So a/2b=$\sqrt{3\\}$

So as a/2b is rational and equal to $\sqrt{3\\}$ so it is a rational number this contradicts as we know that $\sqrt{3} \s$ is irrational.

So 2$\sqrt{3}$ is irrational.

Also in the same way 5$\sqrt{2}$ is also irrational.

So sum of irrationals is irrational.

Hence proven.

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Answer 2

Step-by-step explanation:

Let us suppose that 2√3+√5 is rational. Since , a ,b are integers , is rational,and so √5 is rational. ... Hence , 2√3+√5 is irrational.