Question

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Q.Prove that √2+√5 is irrational .

Answer 1

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Answer 2

Step-by-step explanation:

Let us assume that √2 + √5 is rational.

⇒ √2 + √5 = (a/b)

⇒ √5 = (a/b) - √2

On squaring both sides, we get

⇒ (√5)² = (a/b - √2)²

⇒ 5 = (a/b)² - (2a√2)/b + 2

⇒ 5 - 2 = (a/b)² - (2a√2)/b

⇒ 3 = (a/b)² - (2a√2)/b

⇒ (a/b)² - 3 = (2a√2)/b

⇒ (a² - 3b²)/b² = 2a√2/b

⇒ (a² - 3b²/b²)(b/2a) = √2

⇒ (a² - 3b²)/2ab = √2

Here, √2 is rational number which is a contradiction as we know that √2 is an irrational number.

Therefore, √2 + √5 is an irrational number.

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