Question

Show how 
$\sqrt{5}$

Can be represented on the number line​

Answer 1

Answer:

Again by pythagoras theorem we get OC = root 3.

Then by compus taking radius =OC

, draw an arc so that it cuts the number line at D

. Then the distance OD will be the square root of 3.

Answer 2

Answer:

• Draw number line as shown in the figure.

• Let the point O represent 0 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 = 1 unit

Using pythagoras theorem, we have

${\boxed{ \bf{\sf \: OB = OA + AB}}}$

${\boxed{ \bf{\sf \: {OB}^{2} = {2}^{2} + {1}^{2} = 5}}}$

$\red {\boxed{\bf{ \sf \: OB = \sqrt{5}}}}$

• 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.