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  • (i)Represent geometrically the following numbers on the number line : sqroot 4.5

(i) Represent geometrically the following numbers on the number line : \sqrt{4\cdot 5}
(ii) Represent geometrically the following numbers on the number line : \sqrt{5\cdot 6}
(iii) Presentation of \sqrt{8\cdot 1} on number line :
(iv) Presentation of \sqrt{2\cdot 3} on number line:
 

Answers (1)

(i) Solution. AB = 4.5 units, BC = 1 unit


OC = OD = \frac{5\cdot 5}{2} = 2.75 units
OD2 = OB2 + BD2
\left ( \frac{4\cdot 5}{2} \right )^{2}= \left ( \frac{4\cdot 5}{2} -1\right )^{2}+\left ( BD \right )^{2}
\Rightarrow BD^{2}= \left ( \frac{4\cdot 5+1}{2} \right )^{2}- \left ( \frac{4\cdot 5-1}{2} \right )^{2}
\Rightarrow BD^{2}= 4. 5
\Rightarrow BD= \sqrt{4. 5}

So the length of BD will be the required one so mark an arc of length BD on the number line, this will result in the required length.

(ii) Solution.  Presentation of \sqrt{5. 6} on number line.
Mark the distance 5.6 units from a fixed point A on a given line to obtain a point B such that AB = 5.6 units. From B mark a distance of 1 unit and mark a new point C. Find the midpoint of AC and mark that point as O. Draw a semicircle with center O and radius OC. Draw a line
perpendicular to AC passing through B and intersecting the semicircle at O. Then BD = \sqrt{5\cdot 6}


(iii) Solution
Mark the distance 8.1 units from a fixed point A on a given line to obtain a point B such that AB = 8.1 units. From B mark a distance of 1 unit and mark the new point AB. Find the midpoint of AC and mark a point as O. Draw a semi-circle with point O and radius OC. Draw a line perpendicular to AC passing through B and intersecting
the semicircle at D. Then BD - \sqrt{8. 1}

(iv) Solution
Mark the distance 2.3 units from a fixed point A on a given line. To obtain a point B such that AB = 2.3 units. From B mark a distance of 1 unit and mark a new point as C. Find the midpoint of AC and mark the point as. Draw a line perpendicular to AC passing through B and intersecting the semicircle at D. Then BD = \sqrt{2. 3}

 

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