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3+2√3 is irrational number |
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Answer» 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 3Therefore 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. Let 3+√3 is a rational no. So it is in the form of p/b where q≠0P/b=3+√3=> p/b-3=√3LHS 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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