Question

1. Prove that the following are irrational. i) 1/√2 ii) √3+√5 iii) 6+ √2 iv) √5 v)3 + 2√5 (AS)
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Answer 1

Answer:

i) 1/√2

Let us assume 1/√2 is rational.

So we can write this number as

1/√2 = a/b ---(1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) multiply by √2

both sides, we get

1 = a√2/b

Now, divide by b, we get

b=a√2 or b/a=√2

Here, a and b are integers so, b/a is a rational number,

so √2 should be a rational number.

But √2 is a irrational number, so it is contradictory.

Therefore, 1/√2 is irrational number.

Step-by-step explanation:

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