Karnataka Board Solutions for Chapter: Solved Examples, Exercise 1: exercise 1

A sweetseller has $420$ kaju barfis and $130$ badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the number of that can be placed in each stack for this purpose?

Consider the numbers $4^n$, where $n$ is a natural number. Check whether there is any value of $n$ for which $4^n$ ends with the digit zero.

Find the LCM and HCF of $6$ and $20$ by the prime factorisation method.

Find the HCF of $96$ and $404$ by the prime factorisation method. Hence, find their LCM.

Find the HCF and LCM of $6, 72$ and $120$, using the prime factorisation method.

Prove that $\sqrt{3}$ is irrational.

Show that $5-\sqrt{3}$ is irrational.

Show that $3\sqrt{2}$ is irrational.