Question

prove that 3 +root 2 is an irrational number ​

Answer 1

Answer:

Answer: 3+root2=4.414213562

Step-by-step explanation:

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Answer 2

Yes it is an irrational number
Proof

I will do a proof by method of contradiction

Let us assume that 3+sqrt(2) is rational

then it can be expressed as a ratio, a fraction

3+sqrt(2)=p/q (where p and q are integers such that q is non zero and HCF of p and q is 1.)

sqrt(2)=p/q-3

sqrt(2)=(p-3q)/q

since p and q are integers.
Therefore (p-3q)/q is rational number and this implies sqrt(2) is rational.
but it leads to a contradiction as we know sqrt (2) is irrational.
Therefore our assumption is wrong.
3+sqrt(2) is irrrational