Exercise 2.3 - Chapter 2 Real Numbers 9th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

$\operatorname{Ex} 2.3$
Question 1.
Represent the following irrational numbers on the number line.
(i) $\sqrt{3}$
(ii) $\sqrt{4.7}$
(iii) $\sqrt{6.5}$
Solution:
(i) $\sqrt{3}$

(i) Draw a line and mark a point $\mathrm{A}$ on it.
(ii) Mark a point $B$ such that $A B=3 \mathrm{~cm}$.
(iii) Mark a point $\mathrm{C}$ on this line such that $\mathrm{BC}=1$ unit.
(iv) Find the midpoint of AC by drawing perpendicular bisector of $\mathrm{AC}$ and let it be $\mathrm{O}$.
(v) With $\mathrm{O}$ as center and $\mathrm{OC}=\mathrm{OA}$ as radius, draw a semicircle.
(vi) Draw a line $\mathrm{BD}$, which is perpendicular to $\mathrm{AB}$ at $\mathrm{B}$.
(vii) Now $\mathrm{BD}=\sqrt{3}$, which can be marked in the number line as the value of $\mathrm{BE}=\mathrm{BD}$ $=\sqrt{3}$

(i) Draw a line and mark a point $\mathrm{A}$ on it.
(ii) Mark a point $\mathrm{B}$ such that $\mathrm{AB}=4.7 \mathrm{~cm}$.
(iii) Mark a point $\mathrm{C}$ on this line such that $\mathrm{BC}=1$ unit.
(iv) Find the midpoint of AC by drawing perpendicular bisector of $\mathrm{AC}$ and let it be $\mathrm{O}$.
(v) With $\mathrm{O}$ as center and $\mathrm{OC}=\mathrm{OA}$ as radius, draw a semicircle.
(vi) Draw a line $\mathrm{BD}$, which is perpendicular to $\mathrm{AB}$ at $\mathrm{B}$.
(vii) Now $\mathrm{BD}=\sqrt{4.7}$, which can be marked in the number line as the value of $\mathrm{BE}=$ $\mathrm{BD}=\sqrt{4.7}$

(i) Draw a line and mark a point $A$ on it.
(ii) Mark a point $\mathrm{B}$ such that $\mathrm{AB}=6.5 \mathrm{~cm}$.
(iii) Mark a point $\mathrm{C}$ on this line such that $\mathrm{BC}=1$ unit.
(iv) Find the midpoint of $\mathrm{AC}$ by drawing perpendicular bisector of $\mathrm{AC}$ and let it be $\mathrm{O}$.
(v) With $\mathrm{O}$ as center and $\mathrm{OC}=\mathrm{OA}$ as radius, draw a semicircle.
(vi) Draw a line $\mathrm{BD}$, which is perpendicular to $\mathrm{AB}$ at $\mathrm{B}$.
(vii) Now $\mathrm{BD}=\sqrt{6.5}$, which can be marked in the number line as the value of $\mathrm{BE}=$ $\mathrm{BD}=\sqrt{6.5}$.
 

Question $2 .$
Find any two irrational numbers between
(i) $0.3010011000111 \ldots$ and $0.3020020002 \ldots$
(ii) $\frac{6}{7}$ and $\frac{12}{13}$
(iii) $\sqrt{2}$ and $\sqrt{3}$
Solution:
(i) $0.3010011000111 \ldots$ and $0.3020020002 \ldots$
Two irrational numbers $0.301202200222 \ldots . .0 .301303300333 \ldots . .$

(ii) $\frac{6}{7}$ and $\frac{12}{13}$
$\begin{aligned}
&\frac{6}{7}=0.857142 \ldots \\
&\frac{12}{13}=0.923076
\end{aligned}$
Two irrational numbers between $0.8616611666111 \ldots \ldots, 0.8717711777111 \ldots .$
(iii) $\sqrt{2}$ and $\sqrt{3}$

$\sqrt{3}=1.732 \ldots$
$\therefore$ Two irrational numbers between $1.5155 \ldots .1 .6166 \ldots \ldots$
 

Question $3 .$
Find any two rational numbers between $2.2360679 \ldots . .$ and $2.236505500 \ldots .$
Solution:
Any two rational numbers are $2.2362,2.2363$