Question

check whether 5*3*11 +11 and 5*7+7*3+3 are composite numbers.justify your answer

Answer 1

The composite (prime) number it number, which are divisible only by 1 or by themselves. It is e.g. 2, 3, 5, 7, 11 ...
5 * 3 * 11 + 11 = 11(5 * 3 + 1) - this is no composite number, because it has three different dividers:1, 11 and 16, really has more: 1, 2, 4, 8, 11, 16.

5 * 7 + 7 * 3 + 3 = 35 + 21 + 3 = 59 = only = 1 * 59, because:
√59 ≈ 7.68  If 59 is not divisible by one of composite numbers < √59, this number (59) is composite.
59 no divided by 2 without rest, because 59 isn't even
59 no divided by 3 without rest, because 5+9=14, 1+4=5 is not divisible by 3
59 no divided by 5 without rest, because isn't ending of 5 or 0
59 no divided by 7 without rest

59 is the composite number

Answer 2

The product of prime nos added with a prime no is a composite number. Here 5,3,11,7 are prime numbers.