Question
Represent $\sqrt{3.4},\sqrt{9.4},\sqrt{10.5}$ on the real number line.
✓
Answer
In order to represent $\sqrt{ } 3.5$ on number line, we follow the following steps:
1. Draw a line and mark a point $A$ on it.
2. Mark a point $B$ on the line drawn in step $1$ such that $A B=3.5 cm$.
3. Mark a point c on AB produced such that $BC =1$ unit.
4. Find mid-point of $A C$. Let the mid-point be $O$.
5. Taking $O$ as the centre and $O C=O A$ as radius draw a semi-circle; also draw a line passing through $B$ perpendicular to $OB$. Suppose it cuts the semi-circle at $D$.
6. Taking $B$ as the centre and $B D$ as radius draw an arc cutting $O C$ produced at $E$. Point $E$ so obtained represent $\sqrt{3.5}$.
In order to represent $\sqrt{ 9 . 4 }$ on number line, we follow the following steps:
1. Mark a point $F$ on the line drawn such that $A F=9.4 cm$
2. Mark a point $G$ on $AF$ produced such that $FG =1$ unit.
3. Find mid-point of $AG$. Let the mid-point be $O _1$.
4. Taking $O _1$ as the centre and $O _1 A= O _1 G$ as radius draw a semi-circle. Also, draw a line passing through F perpendicular to $O _1 F$. Suppose it cuts the semi-circle at H
5. Taking F as the centre and FH as radius draw an arc cutting $O _1 G$ produced at I. Point I so obtained represents $\sqrt{9.4}$.
In order to represent $\sqrt{10.5}$ on number line, we follow the following steps:
1. Mark a point $J$ on the line such that $AJ =10.5 cm$.
2. Mark a point $K$ on $AJ$ produced such that $JK =1$ unit.
3. Find mid-point of $A K$. Let the mid-point be $O _2$.
4. Taking $O _2$ as the centre and $O _2 A= O _2 K$ as radius draw a semi-circle. Also, draw a line passing through $J$ perpendicular to $O _2 J$. Suppose it cuts the semi-circle at $L $.
5. Taking J as the centre and JL as radius draw an arc cutting $O _2 K$ produced at M . Point M so obtained represents
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