Terry W. answered • 02/20/15

Experienced Tutor Specializing in STEM Subjects

Mind you I'm not an expert on mathematical proofs but here's a simple take on it:

Suppose that 3*(√2)-5 is a rational number, it can therefore be expressed as a ratio of integers m and n:

3(√2)-5=m/n

Adding 5 to both sides:

3(√2)=m/n+5=m/n+5n/n=(m+5n)/n

Dividing both sides by 3:

√2=(m+5n)/(3n)

Now since both m and n are integers, then both terms (m+5n) and 3n are also integers which means √2 can then be expressed as a ratio of integers (ie it's a rational number). Since we are explicitly told that √2 is not a rational number and therefore cannot be expressed as a ratio of integers, this is obviously false. So therefore, the initial assumption that 3(√2)-5 is a rational number is also false so it must be an irrational number.

Ryan A.

tutor

Wow- the proof explanation was fantastic! Two thumbs up!!

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02/20/15

Levi W.

02/20/15