Embibe Experts Solutions for Chapter: Real Numbers, Exercise 1: CBSE-2021 (Delhi - I)

In the following figure, $DE\parallel BC$, $AD=1 \mathrm{cm}$ and $BD=2 \mathrm{cm}$. What is the ratio of the $ar\left(∆ABC\right)$ to the $ar\left(∆ADE\right)$?

Find a rational number between $\sqrt{2}$ and $\sqrt{3}$.

Find the H.C.F of $1260$ and $7344$ using Euclid's algorithm.

Show that every positive odd integer is of the form $\left(4q+1\right)$ or $\left(4q+3\right)$, where $q$ is some integer.

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

The $HCF$ and $LCM$ of $12, 21, 15$ respectively are

Show that the square of any positive integer cannot be of the form $\left(5q+2\right)$ or $\left(5q+3\right)$ for any integer $q.$

Prove that one of every three consecutive positive integers is divisible by $3$.