**1.** Prove that is irrational.

**Solution:**

Lets prove irrational by contradiction.

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by Jashan

by Jashan

**Theorem: Let p be a prime number. If p divides , then p divides a, where a is a positive integer.**

by Jashan

**7.** 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 go in the same direction. After how many minutes will they meet again at the starting point?

**Solution:**

Sonia drives 18 minutes to drive one round of the field whereas Ravi takes 12 minutes to drive one round of the field.

To know after how many minutes will they meet at the starting point, we need to find LCM of 12 and 18.

**LCM=**Product of the greatest power of each prime factor involved in the numbers

Therefore, they are going to meet at the starting point after 36 minutes.

by Jashan

by Jashan