Question

Show that 2√3 +3 is irrational number, given that √3 is irrational.​

Answer 1

Step-by-step explanation:

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To prove = 2√3 is an irrational number.

We shall prove this by the method of contradiction .

so let us assume to the contrary that 2√3 is a rational number =r

2√3=r

√3=r/2

Now we know that √3 is irrational number.

SO, r/2 has to be irrational to make the equation true .

This is a contradiction to our assumption . Thus our assumption is wrong .

Therefore,2√3 is irrational .

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