Question

prove that 4-5√3 is a irra

Answer 1

Hey friend !!

Here is your answer.

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Let 4-5√3 be rational.

Then , 4-5√3 = a/b , where a & b are coprimes.

Then ,

==> 5√3 = a/b + 3

==> √3 = 1/5(a/b + 3)

==> L.H.S is not equal to R.H.S

Since , our assumption is wrong .Hence , irrational and rational can't be equal .

So , 4-5√3 is irrational.

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Hope it helps.

#pragya_singh

Answer 2

Answer:

4 - 5√3 is irrational number.

Step-by-step explanation:

Let 4 - 5√3 be rational number

4 - 5√3 = a/b ( Where a and b are integers)

-5√3 = a/b - 4

√3 = a - 4/ 5b

a - 4/ 5b is rational. So, √3 is rational. But, it contradicts the fact that a - 4/ 5b is irrational. This situation has arrised because our assumption is wrong. Hence 4 - 5√3 is irrational number.

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