Question

Prove that √3+√4 is an irrational number.

Answer 1

$\huge\mathbb{\underline{QUESTION:-}}$

★ Prove that √3+√4 is an irrational number.

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$\huge\mathbb{\underline{SOLUTION:-}}$

★ Lets assume that : √3 + √4 is rational.

★ √3 + √4 = r , where r is rational

[ Squaring both sides , we get ]

• [√3 + √4 ]² = r²

• 3 + 2√12 + 4 = r²

• 7 + 2√12 = r²

• 2√12 = r² - 6

• √12 = [ r² - 6] / 2

★ R.H.S is purely rational , whereas , L.H.S is irrational.

★ This is a contradiction.

★ This means that our assumption was wrong.

★ Hence , √3 + √4 is irrational.

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Answer 2

Answer:

★ Prove that √3+√4 is an irrational number.

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★ Lets assume that : √3 + √4 is rational.

★ √3 + √4 = r , where r is rational

[ Squaring both sides , we get ]

[√3 + √4 ]² = r²

3 + 2√12 + 4 = r²

7 + 2√12 = r²

2√12 = r² - 6

√12 = [ r² - 6] / 2

★ R.H.S is purely rational , whereas , L.H.S is irrational.

★ This is a contradiction.

★ This means that our assumption was wrong.

★ Hence , √3 + √4 is irrational.

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