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Represent $\sqrt{6},\ \sqrt{7},\ \sqrt{8}$ on the number line.
Given: Numbers $\sqrt{6},\ \sqrt{7},\ \sqrt{8}$.
To do: To represent $\sqrt{6},\ \sqrt{7},\ \sqrt{8}$ on the number line.
Solution:
1. Draw a number line.
2. Mark a Point $A$ on number line such that $OA=2\ units$.
3. Take $AP=1\ unit$
4. On applying pythagoras theorem,
$OP^2=OA^2+AP^2=2^2+1^2=4+1=5\ unit$
$\Rightarrow OP=\sqrt{5}$
5. Take $O$ as centre and with compass, draw an arc with the radius $r=OP$. This arc intersect the number line on $B$.
$OB=OP=\sqrt{5}$.
6. Take $BQ=1\ unit$. $OB=\sqrt{5}$.
$\Rightarrow OQ^2=OB^2+BQ^2=( \sqrt{5})^2+1^2=5+1$
$\Rightarrow OQ=\sqrt{6}$
7. Draw an arc with radius $r=OQ$ which intersects the number line on the point $C$. And $OC=\sqrt{6}$
8. Similarly Draw point $D$ and $E$ on the the number line.
Thus Point $C=\sqrt{6}$, $D=\sqrt{7}$, $E=\sqrt{8}$ are the required points on the number line.
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