Prove that the following are irrational: 6+√2
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Prove that 6 + √2 is an irrational number.
Answer: Given 6 + √2.
To prove: 6 + √2 is an irrational number. Proof: Let us assume that 6 + √2 is a rational number. So it can be written in the form a/b. 6 + √2 = a/b. Here a and b are coprime numbers and b ≠ 0.
Solving. 6 + √2 = a/b. we get, => √2 = a/b – 6. => √2 = (a-6b)/b. ...
6 + √2 is an irrational number. Hence, proved.
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