Q. 53.6( 11 Votes )

Locate and on the number line.

Answer :

(i) 5


We can write 5 as the sum of the squares of two natural numbers: 5 = 1 + 4


5 = 12 + 22


On the number line, take OA = 2 units.



Draw BA = 1 units, perpendicular to OA. Join OB.



By Pythagoras theorem, OB = √5 Using a compass with centre O and radius OB, draw an arc which intersects the number line at the point C. Then, C corresponds to √5.


i.PNG


(ii) 10


We can write 10 as the sum of the squares of two natural numbers: 10 = 1 + 9


10 = 12 + 32


On the number line, take OA = 3 units.



Draw BA = 1 units, perpendicular to OA. Join OB.



By Pythagoras theorem, OB = √10 Using a compass with centre O and radius OB, draw an arc which intersects the number line at the point C. Then, C corresponds to √10.


ii.PNG


(ii). 17


We can write 17 as the sum of the squares of two natural numbers: 17 = 1 + 16


17 = 12 + 42


On the number line, take OA = 4 units.



Draw BA = 1 units, perpendicular to OA. Join OB.



By Pythagoras theorem, OB = √17 Using a compass with centre O and radius OB, draw an arc which intersects the number line at the point C. Then, C corresponds to √17.


iii.PNG


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