Prove that
[tex]3 + 2 \sqrt{5} [/tex]
is irrational.(Without calculating directly)
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Prove that
[tex]3 + 2 \sqrt{5} [/tex]
is irrational.(Without calculating directly)
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let 3 + 2 root 5 is rational
therefore 3 + 2 root 5=a/b(where a and b are co prime integer )
root 5=a-3/2b
because a-3/2b is rational
therefore root 5 will also be rational
but we know that,
root 5 is irrational
that is our assumption is wrong
that is 3+2 root 5 is irrational..
hope it helps uh..anyway
wishing u a beautifull night
At first we know that √5 is an irrational no...
And Now , let 3 +2√5 is a rational no...
3+2√5-3=2√5--------(1)..
{rational -rational =rational}
AQ to eq. (1)2√5 is a rational so...
2√5×1/2=√5---------(2)
{rational × rational = rational}
A/Q to eq. (2) √5 is a rational no..
But we know that √5 is an irrational so, our contradict was wrong and...
2+3√5 is an irrational no....
Hope this will help u......✌✌✌✌✌.....