Question

prove that 5+√3 is irrational given that √3 is irrational
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Answer 1

Answer:

5 + 1.732 = 6.732

6732/1000

its rational

Answer 2

Step-by-step explanation:

Let us assume that 5 - √3 is a rational

We can find co prime a & b ( b≠ 0 )such that

5 - √3 = a/b

Therefore 5 - a/b = √3

So we get 5b -a/b = √3

Since a & b are integers,

we get 5b -a/b is rational, and

so √3 is rational.

But √3 is an irrational number

Let us assume that 5 - √3 is a rational

We can find co prime a & b ( b≠ 0 )such that

∴ 5 - √3 = √3 = a/b Therefore 5 - a/b = √3 So we get 5b -a/b = √3

Since a & b are integers, we get 5b -a/b is rational, and so √3 is rational

but √3 is an irrational number

Which contradicts our statement

∴ 5 - √3 is irrational