Question

show that 5-√3 is irrational.
In brief​

Answer 1

Step-by-step explanation:

Let us assume that 5-√3 is a rational no.

Then 5-√3 =p/q for some integer p and q

5-√3 = p/q

√3=5-p/q

Here 5-p/q is rational no. but √3 is an irrational no.

Therefore, our assumption was wrong

Hence, 5-√3 is an irrational no.

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Answer 2

Answer:

Given 5 - √3

To prove: 5 - √3 is an irrational number.

Proof:

Letus assume that 5 - √3 is a rational number.

So it can be written in the form a/b

5 - √3 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving

5 - √3 = a/b

we get,

=>√3 = a/b +5

=>√3 = (a-5b)/b

=>√3 = (a-5b)/b

This shows (a-5b)/b is a rational number.

But we know that √3 is an irrational number, it is contradictsour to our assumption.

Our assumption 5 - √3 is a rational number is incorrect.

5 - √3 is an irrational number

Hence proved.

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