Represent each of the following on different number lines : 2√3, 2√2, 3+√2, 3-√2 and 2√5 .

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Steps of construction of : 1. Take OA = AB = 1 unit and ∠OAB = 90°, so by pythagoras theorem : ⇒ OB² = OA² + AB² ⇒ OB² = 1² + 1² ⇒ OB² = 1 + 1 ⇒ OB² = 2 ⇒ OB = unit 2. Draw BC = AB = OA = 1 unit and ∠OBC = 90°. 3. By pythagoras theorem : ⇒ OC² = OB² + BC² ⇒ OC² = ⇒ OC² = 2 + 1 ⇒ OC² = 3 ⇒ OC = unit. 4. With point O as center and OC as radius darw an arc which meets the number line at point P. OP = OC = . 5. With P as center and OP as radius draw an arc cutting number line at P', so PP' = OP' = OP + PP' = . Steps of construction of : 1. Mark O of the number line at point 0. 2. On the same number line, mark 1 as point A i.e., take OA = 1 unit 3. At point A, draw AC perpendicular to the number line. 4. From AC, cut AB = 1 unit = OA, then join A and B. Using pythagoras theorem, we get : OB² = OA² + AB² OB² = 1² + 1² OB² = 1 + 1 = 2 OB = . 5. Taking point O as center and OB = as radius, draw an arc which cuts the number line at point P. Clearly, OP = OB = 6. With P as center and OP as radius draw an arc intersecting number line at P'. OP' = OP + PP' = . Steps of construction of 1. Mark O of the number line at point 0. 2. On the same number line, mark 1 as point A i.e., take OA = 1 unit 3. At point A, draw AC perpendicular to the number line. 4. From AC, cut AB = 1 unit = OA, then join O and B. Using pythagoras theorem, we get : OB² = OA² + AB² OB² = 1² + 1² OB² = 1 + 1 = 2 OB = . 5. Taking point O as center and OB = as radius, draw an arc which cuts the number line at point P. Clearly, OP = OB = 6. From point P as center and radius = 3 cm draw an arc intersecting number line at P'. OP' = OP + PP' = . Steps of construction of 1. Mark O of the number line at point 0. 2. On the same number line, mark 1 as point A i.e., take OA = 1 unit 3. At point A, draw AC perpendicular to the number line. 4. From AC, cut AB = 1 unit = OA, then join O and B. Using pythagoras theorem, we get : OB² = OA² + AB² OB² = 1² + 1² OB² = 1 + 1 = 2 OB = . 5. Taking point O as center and OB = as radius, draw an arc which cuts the number line at point P. Clearly, OP = OB = 6. From point O as center and radius = 3 unit draw an arc intersecting number line at P'. PP' = OP' - OP = . Steps of construction of : 1. Mark O of the number line at point 0. 2. On the same number line, mark 1 as point A i.e., take OA = 1 unit 3. At point A, draw AC perpendicular to the number line. 4. From AC, cut AB = 2 unit, then join O and B. Using pythagoras theorem, we get : OB² = OA² + AB² OB² = 1² + 2² OB² = 1 + 4 = 5 OB = . 5. Taking point O as center and OB = as radius, draw an arc which cuts the number line at point P. Clearly, OP = OB = 6. From point P as center and OP as radius draw an arc intersecting number line at P'. OP' = OP + PP' = .

Mathematics

Represent each of the following on different number lines : 2√3, 2√2, 3+√2, 3-√2 and 2√5 .

Rational Irrational Nos

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