Question

Prove that 4-√5 is irrational
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Answer 1

Given:

☛ √5 is irrational

To Prove:

☛ 4 - √5 is irrational

Proof:

Let 4 - √5 be a rational number, hence it can be expressed in the form of p/q where p&q are co-prime integers.

So,

p/q = 4 - √5

4 - p/q = √5

4q - p / q = √5

Here, 4q - p/q is rational but this equals to an irrational number i.e., √5 But this is impossible because a rational number can't be equal to an irrational number So this contradiction arrises because of our wrong assumption,

Hence, 4 - √5 is irrational.

Answer 2

verified my answer.......

since, we know that rational number can be write. into form of p/q .... let 4-√5 Be rational number so we can write it as p/q where p & q are integers and q does not 0 ...

now, p/q = 4-√5

4– p/q = √5

4q-p/q = √5

now, we can see that 4q-p/q is a rational number whereas √5 is a irrational number .....

now, rational no =|= irrational number ..

therefore , our assumption is wrong ...

hence, 4-√5 is a irrational number.....

......Hence proved.....