show that (3+√5) is a irrational number
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nagaraj14:
ooh you really a genius in maths
oh no it's just our teacher who teach us like that
teachers are to teach but learning clearly is very great you know my techer also teaches us but i am not as genius as you
oh no bro all have same ability u are also as like as me
ok ok
give more questions like that of ch 1 tomorrow is my revision test
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Here's your answer
To prove: √3+√5 is irrational
To prove it let us assume it to be a rational number
Rational numbers are the ones which can be expressed in p/q form where p,q are integers and q isn't equal to 0
√3+√5=p/q
√3=(p/q)-√5
Squatting on both sides
3=p²/q²-(2√5p)/q+5
(2√5p)/q=5-3-p²/q²
2√5p/q=(2q²-p²)/q²
√5=(2q²-p²)/q²*q/2p
√5=(2q²-p²)/2pq
As p and q are integers RHS is rational
As RHS is rational LHS is also rational i.e √5 is rational
But this contradicts the fact that √5 is irrational
This contradiction arose because of our false assumption
So √3+√5 is irrational.
Hope it helps!!!
omkara2[maths aryabhatta]
To prove: √3+√5 is irrational
To prove it let us assume it to be a rational number
Rational numbers are the ones which can be expressed in p/q form where p,q are integers and q isn't equal to 0
√3+√5=p/q
√3=(p/q)-√5
Squatting on both sides
3=p²/q²-(2√5p)/q+5
(2√5p)/q=5-3-p²/q²
2√5p/q=(2q²-p²)/q²
√5=(2q²-p²)/q²*q/2p
√5=(2q²-p²)/2pq
As p and q are integers RHS is rational
As RHS is rational LHS is also rational i.e √5 is rational
But this contradicts the fact that √5 is irrational
This contradiction arose because of our false assumption
So √3+√5 is irrational.
Hope it helps!!!
omkara2[maths aryabhatta]
ooh you really a maths master
thnx
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