Question

Prove thai 3 +
5 is irrational​

Answer 1

Answer:

3+ 5 is 9

and 8 is an irrational number

Answer 2

NOTE :- If your questions is to prove 5-√3 is a irrational number so, I had done that proof, but if your question is like 3-√5 or 5+√3 or 3+√5 so continue the procedure and change thhe sign off addition or substraction or change the number as well....

so let's get started ...

Step-by-step explanation:

THOSE REAL NUMBER WHICH HAVE NON TERMINATING AND NON RECURING DECIMAALS ARE CALLED IRRATIONAL NUMBERS.

AND AN IRRATIONAL NUMBER IS A REAL NUMBER THATT CAN NOT BE WRRIITTEN. INN TTHE FORM OF p/q.

Now taking your question ,we have to prove that the number 5-√3 is an irrational number ..(see the note on the top of answer first )

Let's try to verify that the number5-√3 is an irrational number ...

PROOF OF THE IRRATIONALITY OF 5-√3

We can prove the irrationality of 5-√3 by using contradiction method .

Let us assume ,5-√3is a rational number .

So, 5-√3 can be represented in the form of fraction ..

$5 - \sqrt{3} = \frac{p}{q} \\ where \: p \: and \: q \: are \: integers \: \\ and \: q \: not \: equal \: to \: 0 \\ so \: \: 5 - \sqrt{3} = \frac{p}{q} \\ - \sqrt{3} = \frac{p}{q} - 5 \\ \sqrt{3} = 5 - \frac{p}{q}$

Here ,p and q are integers ,so the fraction p/q is a rational number and 5 iis. also a rational number .

So, their difference will also be a rational number .

Therefore ,√3 must be a rational number .

But it contradict the fact that √3 is an irrational number .

therefore ,our assumption is wrong and 5-√3 is an irrational number .....

hope help u ...

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