NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.2 –Part 3
Q4 Given that , find .
Solution:

Given

By the property that



Therefore
Q5 Check whether can end with the digit 0 for any natural number n.
Solution:

If the number ends with the digit zero, then it is divisible by 5

Therefore the prime factorization of contains the prime 5.

This is not possible because the only prime in the factorization of is 2 and 3

And the uniqueness of the fundamental theorem of arithmetic guarantees that these are no other prime in the factorization of .
Hence it is very clear that there is no value of n in natural numbers for which ends with the digit zero.
Q6 Explain why and are composite numbers.
Solution:

Numbers are of two types prime and composite

Prime number can be divided by 1 and only itself.

And composite number have factors other than 1 and it self.
It can be observed that
The given expression has 6 and 13 as its factors
Therefore, it is a composite number.
1009 cannot be factorized further.
Therefore, the given expression has 5 and 1009 as its factors
Hence, it is a composite number.
Q7 There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Solution:

Since they both move in the same direction and at the same time

To find the time when will they both meet together,

It is enough if we find the LCM of 12 and 18




Therefore, Sonia and Ravi will meet again after 36 minutes.