Question

2. Prove that 3 + 2 root
5 is irrational​

Answer 1

Answer:

Let us assume that 3 + 2 root is a rational number.

3 + 2 root 5= p/q wgere p and q are integers and q is not equal to 0

3 + 2 root5 = a / b where a and b are co prime .

2root5 = a / b - 3

but as we kniw root 5 is irriational so this contradicts the fact that root 2 is rational . This is because of our wrong assumption that 3 + 2root 5 is rational .

Answer 2

Answer:

Step-by-step explanation:

let us assume 3+2√5 is a rational no.

then we can find co-prime x and y(y≠0)

such that,3+2√5 =x/y

2√5=x/y - 3

√5=1/2(x/y - 3)

sice x and y are integers,thus 1/2(x/y - 3) is a rational number

therefore,√5 is a rational number.but this contadicts the fact that √5 is a irrational number.

so we conclude

3+2√5 is a irrational number

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