Question 6
Represent geometrically the following number on the number line
(i) $\sqrt{4.5}$
(ii) $\sqrt{5.6}$
(iii) $\sqrt{8.1}$
(iv) $\sqrt{2.3}$
Thinking process
(i) Firstly, we draw a line segment AB of length equal to the number inside the root and extend it to C such that BC = 1.
(ii) Draw a semi-circle with centre O ( O is the midpoint of AC ) and radius OA.
(iii) Now, draw a perpendicular line from B to cut the semicircle at D.

(iv)Further, draw an arc with centre B and radius BD meeting AC produced at E.

Open in App

Solution

(i) Firstly, we draw a line segment AB = 4.5 units and extend it to C such that BC = 1 unit. Let O be the mid-point of AC.
Now, draw a semi-circle with centre O and radius OA. Let us draw BD perpendicular to AC Hence, the distance BD is $\sqrt{4.5}$ units
Draw an arc with centre B and radius BD, meeting AC produced at E, then
$B E = B D = \sqrt{4.5}$ units

(ii) Firstly, we draw a line segment AB = 5.6 units and extend it to C such that BC = 1 unit. Let O be the mid-point of AC.
Now, draw a semicircle with centre O and radius OA. Let us draw BD perpendicular to AC. Hence , the distance BD is $\sqrt{5.6}$ units.
Draw an arc with centre B and radius BD, meeting AC produced at E, then BE =BD = $\sqrt{5.6}$ units.

(iii) Firstly, we draw a line segment AB = 8.1 units and extend it to C such that BC = 1 unit, let O be the midpoint of AC.
Now, draw a semicircle with centre O and radius OA.
Let us draw BD perpendicular to AC passing through the point B intersecting the semi-circle at point D.
Hence, the distance BD is $\sqrt{8.1}$ units.
Draw an arc with centre B and radius BD, meeting AC produced at E, then
$B E = B D = \sqrt{8.1}$ units

(iv) Firstly, we draw a line segment AB = 2.3 units and extend it to C such that BC = unit. Let O be the mid-point of AC.
Now, draw a semi-circle with centre O and radius OA.
Let us draw BD perpendicular to AC passing through point B and intersecting the semi-circle at point D.
Hence the distance BD is $\sqrt{2.3}$ units
Draw an arc with centre B and radius BD, meeting AC produced at E, then $E = B D = \sqrt{2.3}$ units.

Suggest Corrections

Similar questions

Q. Question 6
Represent geometrically the following number on the number line
(i)

\sqrt{4.5}

(ii)

\sqrt{5.6}

(iii)

\sqrt{8.1}

(iv)

\sqrt{2.3}

Thinking process
(i) Firstly, we draw a line segment AB of length equal to the number inside the root and extend it to C such that BC = 1.
(ii) Draw a semi-circle with centre O ( O is the midpoint of AC ) and radius OA.
(iii) Now, draw a perpendicular line from B to cut the semicircle at D.

(iv)Further, draw an arc with centre B and radius BD meeting AC produced at E.

Q. To construct a trapezium ABCD with

A B ∥ C D,

AB = 8 cm, BC = 5 cm, AD = 6 cm and

∠ A B C = 60^{\circ},

we follow the following steps:
1) Draw the line segment AB = 8 cm.
2) Construct the angle

∠ A B X = 60^{\circ}

at B.
3) With B as centre, draw an arc of radius 5 cm cutting BX at C.

The next step is ___.

Q. Steps for the construction of

90^{\circ}

is given below. Choose the correct order.

1.With P as the centre and radius more than half of PQ, draw an arc above the line segment AB
2.With O as the centre, draw semicircle with suitable radius that cuts line segment AB at point P and Q.
3.With Q as the centre and with same radius as in previous step, draw another arc, which cuts the previous arc. Name the point of intersection as C
4.Draw a line segment AB, mark a point 'O' on it.
5.Join points O and C using a scale and a pencil and extend to get ray OC

Q. Draw a circle with centre O and any radius. Draw AC and BD two perpendicular diameters of the circle. Join AB, BC, CD and DA.

Pavan tried to draw a line parallel to a given line, 'l'. Few steps are shown below. What will be the next step?

Step 1: Mark a point A, not on the line 'l'.
Step 2: Mark point B on line 'l'.
Step 3: Draw line segment joining points A and B.
Step 4: Draw an arc with B as the centre, such that it intersects line 'l' at D and AB at E.

Join BYJU'S Learning Program