Question

Prove that √3 + √5 is irrational.​

Answer 1

Answer:

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Answer 2

Answer:

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 a irrational number.

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

Step-by-step explanation:

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