Q. 53.6( 11 Votes )

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(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.

(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). 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.

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