Question

Prove that 7+√3 is Irrational​

Answer 1

Here we go

We will prove it by contradiction

Let 7+√3 be rational no

So, 7+√3= p/q

√3 = p/q-7

√3 = p-7q/q

But this can't be possible

Therefore, 7+√3 is iraational

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Answer 2

Answer:

Step-by-step explanation:

Let us assume to the contrary that 7+√3 is rational .

: 7 + √3  = a/b ( where a and b are integers , b ≠ 0 , and a and b are co - prime)

⇒ √3 = a/b - 7

⇒ √3 =a - 7b/b

since , a and b are integers , thus a/b - 7 is rational and so √3 is also rational . But this contradicts the fact that √3 is irrational . Thus our assumption is wrong that 7 + √3 is rational .

HENCE WE PROVED THAT  7 + √3 IS IRRATIONAL

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