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7√5+3√5 prove it irrational |
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Answer» Let 7√5+3√5 is rational number Then, 7√5+3√5=p÷q. (p and q are the integer which has no other factor expect 1 and q is not equal0)Or,. √5(7+3)=p÷qOr,. √5=(p÷q)÷(7+3) Here, (p÷q)÷(7+3) is a rational no. which is equal to a irrational no. So,our contraction was wrong . HENCE,7√5+3√5 is irrational no. 10√5=a/bThen.√5=a/10bSo √5 is a rational as a,b,10 are rational no.,But it is a contradiction to the fact that √5 is an irrational no.Thus,7√5+3√5 is irrational number.Hence ,proved |
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