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Prove that 3+5√2 is irrational. |
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Answer» Let us assume that 3+5√2is rational no. written in the form of p/q where p,q are integer.Suppose p,q have no any common factor .3+2√5=p/q5√2=p/q-3√2 =1/5(p/q-3)Since, 1/5(p/q-3)is rational So, √2 is also a rational .This is contradicts the fact that √2 is irrational.Hence, 3+2√5 is irrational. Let 3+5√2 is a rational numberThen,3+5√2=p/q( rational number always in the form of p/q where q not equal to \'0\')3+5√2=p/q5√2=p/q-3√2=p/q-3/5But we know that √2 is an irrational no° .So , 3+5√2 is an irrational number. |
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