Question

how to prove that under root 3 + under root 5 is an irrational number​

Answer 1

Answer:

We have to prove that $\sqrt{3\\} +\sqrt{5$ is irrational number.

Step-by-step explanation:

Let us assume that $\sqrt{3} +\sqrt{5}$ is rational number.

It can be written in form of  $\frac{p}{q}$ where q$\neq$0 and p,q are integers ; HCF(p,q) = 1

PICTURE

We know that $\sqrt{6}$ is irrational number and RHS side is rational.

therefore, it is contradiction and our assumption is false.

Hence $\sqrt{3} +\sqrt{5}$ is irrational number.

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