Question
Write four rational numbers between $\sqrt{2}$ and $\sqrt{3}$
✓
Answer
Since squares of $\sqrt{2}$ and $\sqrt{3}$ are $2$ and $3$ respectively.
Now, find four rational numbers between $2$ and $3$ such that each of them is a perfect square.
Let the numbers be $2.25,2.4025,2.56,2.89$,
where,
$\sqrt{2.25}=1.5$
$\sqrt{2.4025}=1.55$
$\sqrt{2.56}=1.6$
$\sqrt{2.89}=1.7$
Hence, required rational numbers between $\sqrt{2}$ and $\sqrt{3}$ are $1.5,1.55,1.6$ and $1.7 .$
Now, find four rational numbers between $2$ and $3$ such that each of them is a perfect square.
Let the numbers be $2.25,2.4025,2.56,2.89$,
where,
$\sqrt{2.25}=1.5$
$\sqrt{2.4025}=1.55$
$\sqrt{2.56}=1.6$
$\sqrt{2.89}=1.7$
Hence, required rational numbers between $\sqrt{2}$ and $\sqrt{3}$ are $1.5,1.55,1.6$ and $1.7 .$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A rectangular water$-$tank measuring $80 \ cm \times 60\ cm$ is filled form a pipe of cross$-$sectional area $1.5 \ cm^2$, the water emerging at $3.2 m/s$. How long does it take to fill the tank?
→In the given figure, $\triangle A B C$ is right angled at $B . A D$ divides $B C$ in the ratio $1: 2$. Find$\text { (i) } \frac{\tan \angle BAC }{\tan \angle BAD } \text { (ii) } \frac{\cot \angle BAC }{\cot \angle BAD }$
→Solve the following systems of equation by using the method of cross multiplication:
$2 x+3 y=17,3 x-2 y=6$
→$2 x+3 y=17,3 x-2 y=6$
$ABCD$ is a trapezium with $AB \| DC$. A line parallel to $AC$ intersects $AB$ at point $M$ and $BC$ at point $N$.Prove that: area of $\triangle ADM =$ area of $\triangle ACN.$
→Construct a triangle using the given data: $DE = 6.5\ cm, EF = 5.8\ cm$ and $DF = 4.2\ cm$
→A man sold a chair and a table for ₹ 2178, thereby making a profit of 12% on the chair and 16% on the table. By selling them for ₹ 2154, he gains 16% on the chair and 12% on the table. Find the cost price of each.
Find the area of the biggest circle that can be cut from a rectangular piece $44\ cm$ by $28\ cm$. also, find the area of the paper left after cutting out the circle.
→A closed box is made of wood $5\ mm$ thick. The external length, breadth and height of the box are $21 \ cm$, $13 \ cm$ and $11 \ cm$ respectively. Find the volume of the wood used in making the box.
→In $\triangle ABC, D$ and $E$ are the mid$-$point on $AB$ and $AC$ such that $DE \| BC$.If $AD : BD = 4 : 5$ and $EC = 2.5 \ cm$, find $AE.$
→Find the $M.P.$ in the following:$S.P. =Rs. 1892,$ Discount $=14\%$
→