show that 5+2root 7 is irrational number where root 7 is given to be an irrational numbers
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Answer:
Step-by-step explanation:
Let, 5+2√7 be rational.
Therefore, 5+2√7 =a/b where a and b are integers having no common factors other than 1.
Now, 5+2√7=a/b
=>2√7=a/b-5
=>2√7=a-5b/b
=>√7=a-5b/2b
Since, a and b are integers, therefore, √7 is rational. This contradicts the fact that √7 is irrational. Therefore, our assumption was wrong. Hence, 5+2√7 is irrational.
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the answer above is correct
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