Question

give that √3 is irrational l, prove that 5√3-2 is an irrational number​

Answer 1

Answer:

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Given : √3 is irrational

To Prove : 5√3 - 2 is an irrational number

Proof :

let be assume that 5√3 - 2 is a rational number

∴ it can be written in the form of a/b

∴ 5√3 - 2 = a/b

5√3  = a/b + 2

√3 = a + 2b/5b

a + 2b/5b is a rational number

therefore, √3 is also a rational number

but it is given that √3 is an irrational number

∴ our assumption is wrong and 5√3 - 2

  is an irrational number.

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Step-by-step explanation: