Question

prove that 3+ ✓2 is an irrational number​

Answer 1

$\mathcal{\huge{\underline{\underline{\red{Question}}}}}$

✳ Prove that 3+ ✓2 is an irrational number .

$\mathcal{\huge{\underline{\underline{\green{Solution:-}}}}}$

⬛ Let 3+√2 is an rational number.

↪ Such, that 3+√2 = a/b ,where a and b are integers and b is not equal to zero .

▶Therefore,

3 + √2 = a/b

➡√2 = a/b -3

➡√2 = (3b-a) /b

⏩Therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers.

⏩It means that √2 is rational.

⏩But this contradicts the fact that √2 is irrational.

✒So, it concludes that 3+√2 is irrational.✅

$\mathcal{\large {\fbox{\fbox{\pink{Hence\:proved.}}}}}$

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