Question

Prove that 6+√2 is an irrational number.

Answer 1

Answer:

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Step-by-step explanation:

(iii) Let take that 6 + √2 is a rational number.

So we can write this number as

6 + √2 = a/b

Here a and b are two co prime number and b is not equal to 0

Subtract 6 both side we get

√2 = a/b – 6

√2 = (a-6b)/b

Here a and b are integer so (a-6b)/b is a rational number so √2 should be a rational number But √2 is a irrational number so it is contradict

Hence result is 6 + √2 is a irrational number