Question

Prove that √5 - √3 is an irrational number​

Answer 1

Answer:

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Step-by-step explanation:

Let √5 - √3 be a rational number , say r

then √5 - √3 = r

On squaring both sides,

(√5 - √3)² = r²

5 - 2√15 - 3 = r²

2 - 2√15 = r²

2√15 = r² + 2

√15 = (r² + 2)/2

Now (r2 + 2) / 2 is a rational number and √15 is an irrational number .

Since a rational number cannot be equal to an irrational number . Our assumption that is √5-√3 rational wrong .