Embibe Experts Solutions for Chapter: Real Numbers, Exercise 1: Exercise

On dividing $6\sqrt{27}$ by $2\sqrt{3}$, the number to be obtained is _____.

The number $\frac{\sqrt{5}+2}{\sqrt{5}-2}$ is

Every composite number can be expressed as a product of

Prove that $\sqrt{2}$ is an irrational number.

Euclid's division lemma states that for any two positive integers $a$ and $b$ there exist unique integers $q$ and $r$ such that $a=bq+r,$ where $r$ must satisfy

Use Euclid's division lemma to show that the cube of any positive integer is either of the form $9m, 9m+1$ or $9m+8$ for some integer $m$.

Find the $\mathrm{HCF}$ of the following using Euclid Division lemma.

$1860$ and $2015$

Show that any positive odd integer is of the form  $6q+1$, $6q+3$, and $6q+5$, where $q$ is some positive integer.