Question

prove 2+ root 5 is an irrational number ​

Answer 1

Answer:

let us assume that 2+√5 is rational number

in the form of p/q qis not equal to 0

Step-by-step explanation:

1. √5 p/q -2
2. √5-2q/q
3. but √5 is irrational number
4. this leads to our contradiction our assumption is wrong
5. 2+√5 is irrational number.
6. HENCE IT IS PROVED ..

Answer 2

Step-by-step explanation:

let us assume that 2+root 5 is an rational number

let 2and 5 be in the form of p/q

where p ana q are coprimes

by dividing both the sides

root 2=q/5p

root 5 is also a rational number

but this contradiction to the fact that root 5 is an irrational number

this contradiction is raised Becoz assuming that 2+root 5 is a rational number

therefore ,our assumption is wrong

therefore ,2+root5 is an irrational number

hence proved

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