Question

Show that√3+ 4 is an irrational number.

read the question carefully there is root in only 3 not in 4.​

Answer 1

Answer:

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Answer 2

Answer:

let assume √3+4 is rational number

√3+4=r where r is rational

squaring both the side

(√3+4)²=r²

(√3)²+4²+8√3=r²

3+16+8√3=r²

8√3=r²-19

√3=(r²-19)/8

hence RHS is rational but LHS is irrational

this contradiction fact that our assumption is wrong

√3+4 is an irrational number.

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