Question

1.Can the number 6", n being a natural number, end with the digit 5? Give reason.
2.Is 7 x 5 x 3 x 2 +3 a composite number? Justify your answer.
3.Prove that (2 (root 3)+root 5) is an irrational number. Also check whether (2 (root 3)+root 5) (2(root 3) - root5) is rational or irrational.​

Answer 1

Answer:

1. 6 cannot be written in the form of 2^m X 5^n. So, 6 ^n cannot end with five. And for, 6n. This too can't end with five, as all multiples of 6 end only with 0, 2,4, 6,8.
2. It is a composite number. Step-by-step explanation: The said number will be a composite number, since the product 7×5×3×2 is divisible by 3 so the number 7×5×3×2 +3 will also be divisible by 3 hence it would be a composite number.
3. It is in photo above⬆