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3+2√3 is irrational number

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3+2√3 is irrational number

Posted by Om Yadav 4 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Devika Sasidharan 4 years, 5 months ago

Assume that 3+2 root 3 is rational. 3+2 root 3=a/b (3-a)/b=2 root 3 (3b-a)/b=2 root 3 (3b-a)/2b=root 3 Therefore our assumption is wrong,(3b-a)/2b is a rational number which implies that root 3 is irrational. Therefore,3+2 root 3 is irrational.

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Anup Kumar Sahu 4 years, 5 months ago

Let 3+√3 is a rational no. So it is in the form of p/b where q≠0 P/b=3+√3 => p/b-3=√3 LHS is a rational no, so RHS should be rational, But we know that √3 is irrational. This contradicts to the fact that 3+√3 is rational. Hence 3+√3 is irrational.

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CBSE > Class 10 > Mathematics