

InterviewSolution
Saved Bookmarks
1. |
Show that 5 + √7 is an irrational number. |
Answer» Let us assume that 5 + √7 is a rational number. So, we can find co-prime integers ‘a’ and ‘b’ (b ≠ 0) such that \(5+\sqrt7 = \frac{a}{b}\) \(\therefore \sqrt7 = \frac{a}{b} - 5\) Since, ‘a’ and ‘b’ are integers,\( \sqrt[a]b \) – 5 is a rational number and so √7 is a rational number. ∴ But this contradicts the fact that √7 is an irrational number. Our assumption that 5 + √7 is a rational number is wrong. ∴ 5 + √7 is an irrational number. |
|