Question

Represent √3 and - √5 on the number line.​

Answer 1

Answer:

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Answer 2

For diagram refer to above picture

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√3 on the number line

Construct BD of 1 unit length perpendicular to OB as fig. Join OD

$By \: \: Pythagoras \: \: theorem, \: \: \\ \: \: \: \: \: \: \: \: \: OD= \sqrt{( { \sqrt{2}) }^{2} + {(1)}^{2} } \\ \\ = \sqrt{2 + 1} \\ \\ = \sqrt{3}$

• Using a compass, with centre O and radius OD, draw an arc which

• intersects the number line at the point L right side to 0. Then ′L′ corresponds to √3.

Hence we have located √3 on the number line .

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√5 on the number line

• Draw number line as shown in the figure.

• Let the point O represent 0(zero) and point A represents 2.

• Draw perpendicular AX at A on the number line and cut-off arc AB=1unit.

• We have OA=2 units and AB=1unit

Using pythagoras theorem, we have,

$OB² =OA²+AB²$

$OB² =(2)²+1² =5$

$OB=√5</p><p>$

Taking O as the centre and OB= √5. as radius draw an arc cutting real line at C. Clearly, OC=OB= √5

Hence, C represents √5 on the number line.