Prove that root 2+3 is a irrational.

1.	Prove that root 2+3 is a irrational.
Answer» If possible let {tex}3 + \\sqrt { 2 }{/tex} is rational number, and we take another rational number 2 for our calculation.{tex}\\Rightarrow ( 3 + \\sqrt { 2 } ) - 3 = \\sqrt { 2 }{/tex}\xa0( difference of two rational number is a rational number){tex}\\therefore \\sqrt { 2 }{/tex} is rationalThis contradicts the fact that {tex}\\sqrt { 2 }{/tex} is irrationalSince the contradiction arises by assuming that {tex}3 + \\sqrt { 2 }{/tex} is rational.Hence, {tex}3 + \\sqrt { 2 }{/tex} is irrational.

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