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Prove that 5-root3 is irrational |
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Answer» If possible root 5 is rational no.5=p/q( where q not equal 0 ,, p/q having no factors other than 1)Squaring both sides5=P2/q2P2=5q2....1P2 is divisible by5 P is also divisible by 5Putting p=5 in 1(5m)2=5q225m2=5q25m2 =q2q2 is divisible by 5q is also divisible by 55 is common factors of p and qThis is contradictionSo,our assumption is wrong Root 5 is irrational no. Let us assume the given number be rational and we will write the given number in p/q form⇒5− 3\u200b = qp\u200b ⇒ 3\u200b = q5q−p\u200b We observe that LHS is irrational and RHS is rational, which is not possible. This is contradiction. Hence our assumption that given number is rational is false ⇒5− 3\u200b is irrational I know anwer but can\'t type sorry soory |
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