Question

Represent the number √5 and√10 on a
To on a number line​

Answer 1

Answer:

Draw a number line. Mark O as the zero on the number line. Step 2: At point A, draw AB ⊥ OA such that AB = 1 unit. Step 3: With point O as the centre and radius OB, draw an arc intersecting the number line at point C.

Answer 2

Step-by-step explanation:

i. Draw a number line and take point A at 2.

  Draw AB perpendicular to the number line such that

AB = 1 unit. 

In ∆OAB, m∠OAB = 90°  ∴ (OB)2 = (OA)2 + (AB)2 … [Pythagoras theorem] 

= (2)2 + (1)2  ∴ (OB)2 = 5  ∴ OB = √5 units. …

[Taking square root of both sides] 

With O as centre and radius equal to OB,

(DIAGRAM 1ST)...........

draw an arc to intersect the number line at C. The coordinate of the point C is √5. ii.

Draw a number line and take point Pat 3. 

Draw PR perpendicular to the number line such that

PR = 1 unit. 

In ∆OPR, m∠OPR = 90°  ∴ (OR)2 = (OP)2 + (PR)2 …

[Pythagoras theorem]

= (3)2 + (1)2  ∴ (OR)2 = 10  ∴ OR = √10units. …

[Taking square root of both sides] 

(DIAGRAM 2nd)........

With O as centre and radius equal to OR, draw an arc to intersect the number line at Q.

The coordinate of the point Q is √10