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Prove that √2 + √5 is irrational . |
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Answer» let us ASSUME √2+√5 is a RATIONAL number we can find a,b are Co primed √2+√5=a/b squaring on both SIDES (√2+√5)^= (a/b)^ 2+5+2(√2)(√5)= a^/b^ 7+2√10=a^/b^ 2√10= a^/b^ -7 2√10 = a^-7b^/b^ √10=a^-7b^/2b° if a,b are INTEGER than RHS rational if RHS is rational than LHS √10 is rational But this is a FACT that √10 is irrational √10 is irrational √2+√5 is irrational. hope this help you |
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