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Prove that √3+√5 is an irrational​

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Let √3 + √5 be a RATIONAL number , say r

then √3 + √5 = r

On SQUARING both sides,

➡(√3 + √5)² = r²

➡3 + 2 √15 + 5 = r²

➡8 + 2 √15 = r²

➡2 √15 = r2 - 8

➡√15 = (r2 - 8) / 2

Now (r2 - 8) / 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 √3 + √5 is rational wrong .


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