Question

prove that 3- 7√3 is irrational

Answer 1

Here Is Your Ans ⤵

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Let , 3 - 7√3 is an rational number

➡ 3 - 7√3 = A / B

➡ - 7√3 = A / B + 3

➡ √3 = A / -7B + 3

integer = Fraction

So , our assumptions is Wrong 3 - 7√3 is an irrational number

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Answer 2

let, 3+7√3 a rational number.

therefore, 3+7√3=a/b

=>7√3=a/b-3

=>√3=1/7(a/b-3)

since, a/b is a rational number

therefore, a/b-3 is also a rational number

similarly, 1/7(a/b-3) is also rational number

and √3 is an irrational number

but, we know that, a rational number is never equal with an irrational number.

hence, our assumption was wrong.

therefore, 3-7√3 is an irrational number.

hope it helps you ☺☺