Question

Prove that√3 -7 is an irrational number

Answer 1

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Let the √3 is rational so it can be written in the form of p/q where p and q are co prime

√3=a/b

squaring on both sides we get

3=a²/b²

3b²=a²

hence a²divide 3b² so it also divide 3b

now le a =3c

3b²=(3c)²

3b²= 9c²

hence 3b² divide 9c² and hence 9c

thus a and b are not co prime

hence √3 is irrational❤️

Answer 2

Answer:

Let the √3 is rational so it can be written in the form of p/q where p and q are co prime

√3=a/b

squaring on both sides we get

3=a²/b²

3b²=a²

hence a²divide 3b² so it also divide 3b

now le a =3c

3b²=(3c)²

3b²= 9c²

hence 3b² divide 9c² and hence 9c

thus a and b are not co prime

hence √3 is irrational

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