Question

Prove that (√3+√2) 2 is irrational number. Step by step

Answer 1

Answer:

Let as assume that √2 + √3 is a rational number .

Then , there exists co - prime positive integers p and q such that

Step-by-step explanation:

√2+√3=p/q

=p/q-√3=√2

squaring on both sides,we get

=[p\q-√3]²=(√2)²

=p²/q²-2p/q√3+3=2

=p²/q²+3-2=2√3p/q

=p²/q²+1=2√3p/q

=(p²+q²/q²)×q/2p=√3

=p²+q²/2pq=√3

=√3is a rational number.

This contradicts the fact that √3 is irrational .

so assumption was incorrect . Here √2 + √3 is irrational.

Answer 2

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