Question

show that 5 + 2 root 7 is an irrational number where root 7 is given to be an irrational number

Answer 1

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.

Answer 2

Answer:

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