give that under root 2 is irrational prove that 5+3 under root 3 is irrational number
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hope this help........
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GovindRavi:
opps sorry wrong post...you can check my profile for the solution of same problem...sorry for inconvenienve
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!!! Hi friends !!!
let 5+3√3 be rational
5+3√3 = a / b [where a and b are co prime nos]
3√3 = a / b - 5
3√3 = a- 5b / b
√3 = a- 5b / 3b
∴ a- 5b / 3b is rational
∴ √3 is also rational
this contradiction has arisen because of our wrong assumption that 5 + 3√3 is rational
∴ 5 + 3√3 is irrational
(or)
let 5+3√2 be rational
5+3√2 = a / b [where a and b are co prime nos]
3√2 = a / b - 5
3√2 = a- 5b / b
√2 = a- 5b / 3b
∴ a- 5b / 3b is rational
∴ √2 is also rational
but it is given that √2 is irrational
this contradiction has arisen because of our wrong assumption that 5 + 3√2 is rational
∴ 5 + 3√2 is irrational
Hence proved.......... ;D
***************************************************************************************
Hope this helps.................. :D
let 5+3√3 be rational
5+3√3 = a / b [where a and b are co prime nos]
3√3 = a / b - 5
3√3 = a- 5b / b
√3 = a- 5b / 3b
∴ a- 5b / 3b is rational
∴ √3 is also rational
this contradiction has arisen because of our wrong assumption that 5 + 3√3 is rational
∴ 5 + 3√3 is irrational
(or)
let 5+3√2 be rational
5+3√2 = a / b [where a and b are co prime nos]
3√2 = a / b - 5
3√2 = a- 5b / b
√2 = a- 5b / 3b
∴ a- 5b / 3b is rational
∴ √2 is also rational
but it is given that √2 is irrational
this contradiction has arisen because of our wrong assumption that 5 + 3√2 is rational
∴ 5 + 3√2 is irrational
Hence proved.......... ;D
***************************************************************************************
Hope this helps.................. :D
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