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Prove root3+2 is irrational

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Prove root3+2 is irrational

Posted by Darshanathish Sarvesh 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 4 years, 8 months ago

Let 2+√3 is a rational number.
A rational number can be written in the form of p/q.
2+√3=p/q
√3=p/q-2
√3=(p-2q)/q
p,q are integers then (p-2q)/q is a rational number.
But this contradicts the fact that √3 is an irrational number.
So,our supposition is false.
Therefore,2+√3 is an irrational number.
Hence proved.

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