Question

Represent geometrically the following numbers on the number line: √4.5 √8.3. (step by step explanation preferably done in notebook please) I’ll mark the best answer as brainliest

Answer 1

Answer:

To represent geometrically √x on a number line:

• Draw a line segment AB with length x  (where point A is -x and point B is zero on the number line).
• Extend AB by drawing a line segment BC of length 1 unit.
• Draw a line perpendicular to AC at point B.
• Let O be the midpoint of AC.
  Draw a semicircle with center O and radius OA.
• Let point D be where the semicircle intersects with the perpendicular line.  BD = √x
• Draw an arc with center B and radius BD from point D to the number line.
• BE = √x ⇒ point E = √x on the number line.

Attachment 1

To represent geometrically √4.5 on a number line:

Draw:

• Point A = -4.5
• Point B = 0
• Point C = 1

Draw a line perpendicular to AC at point B.

Let O be the midpoint of AC:

$\implies \sf O=\dfrac{-4.5+1}{2}=-1.75$

Draw a semicircle with center O and radius OA

$\implies \sf OA=\dfrac{AC}{2}=\dfrac{5.5}{2}=2.75$

Let point D be where the semicircle intersects with the perpendicular line

$\implies \sf BD=\sqrt{AB}=\sqrt{4.5}$

Draw an arc with center B and radius BD from point D to the number line.

$\implies \sf BE=\sqrt{4.5}$

⇒ Point E is $\sf \sqrt{4.5}$ on the number line.

Attachment 2

To represent geometrically √8.3 on a number line:

Draw:

• Point A = -8.3
• Point B = 0
• Point C = 1

Draw a line perpendicular to AC at point B.

Let O be the midpoint of AC:

$\implies \sf O=\dfrac{-8.3+1}{2}=-3.65$

Draw a semicircle with center O and radius OA

$\implies \sf OA=\dfrac{AC}{2}=\dfrac{9.3}{2}=4.65$

Let point D be where the semicircle intersects with the perpendicular line

$\implies \sf BD=\sqrt{AB}=\sqrt{8.3}$

Draw an arc with center B and radius BD from point D to the number line.

$\implies \sf BE=\sqrt{8.3}$

⇒ Point E is $\sf \sqrt{8.3}$ on the number line.