Question

prove that 2+3√5 is an irrational number​

Answer 1

Step-by-step explanation:

Let x=2+3 √5 be a rational number.

3 √5 =2+x

√5 = 2+X/3

Since x is rational, 2+x is rational and hence

2+x/3 is also rational number

⇒ √5 is a rational numbers, which is a contradiction.

Hence 2+3√5 must be an irrational number.

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Answer 2

Step-by-step explanation:

2+3root5=p/q

then 3root5=p/q-2

squaring on both sides

$({3}^{2}) ( { \sqrt{5} }^{2} ) = p lq$