prove that √2 is an irrational number and hence show that 3_√2 is also an irrational number
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Hii There!!
Let us assume to the contrary that 3-√2 is rational
=) 3-√2=p/q
=)-√2=p/q-3
=) -√2 = p-3q/q
=)√2=.- [p-3q/q]
=) but, this contradicts the fact that √2 is irrational.
Hence, 3-√2 is irrational.
Hope it helps
Let us assume to the contrary that 3-√2 is rational
=) 3-√2=p/q
=)-√2=p/q-3
=) -√2 = p-3q/q
=)√2=.- [p-3q/q]
=) but, this contradicts the fact that √2 is irrational.
Hence, 3-√2 is irrational.
Hope it helps
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