Question

1. Show that 7x11x13+13 is a composite number.
2. Prove that 6 - V5 is irrational.
3. Prove that V3 is irrational.​

Answer 1

1)7×11×13+13

=13(7×11+13)

13(77+1)

13×78

since it has more than one factor it is composite

2)Let us assume that 6-√5is rational

such that 6-√5=a/b,where a and b belong to integer and are co prime

so ,-√5=a/b-6

since a/b-6 is rational but -√5 is irrational

therefore 6-√5 is irrational

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