Question

Represent $\sqrt{9.3}$on number line!!

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Answer 1

Solution:-

(In the first attachment)

Let's consider a semi-circle. If we choose $C$ from the circumference, $\triangle ABC$ is always a right triangle.

Let's draw a leg from $C$. It will be $\overline{CH}$.

After producing the leg we see three right triangles, and all three are similar to each other.

Here, we will choose two right triangles below.

$\rightarrow \triangle ACH\sim \triangle CBH\ \mathrm{(\because AA\ Postulate)}$

The corresponding sides are equal in ratio.

$\rightarrow \overline{AH}:\overline{CH}=\overline{CH}:\overline{BH}$

$\rightarrow \overline{CH}^2=\overline{AH}\cdot \overline{BH}$ [Eqn. 1]

This is the relation of the three sides.

If we choose $\overline{AH}=9.3$ and $\overline{BH}=1$, according to [Eqn. 1] we have $\overline{CH}=\sqrt{9.3}$. So, it is possible to represent it on a number line.

Method:-

We see that $\sqrt{9.3}$ is the length of one side. To represent it, we first put $H$ at the origin.

Then draw $\overline{AH}=9.3$ on to the left and $\overline{BH}=1$ on to the right of the origin. And then let $\overline{AB}$ be the diameter of the semi-circle.

After we draw a semi-circle, let's produce a leg from $H$. The length of the leg inside the circle is $\overline{CH}=\sqrt{9.3}$.

Let's draw it on to the right of the origin. We're done!

Learn More:-

• Geometric Mean

(In the second attachment)

If a circle's radius is divided into $a,b$ the length of the green line will be $\sqrt{ab}$. We call this the geometric mean, for short the G.M.

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Answer 2

Answer:

How can I plot root 9.3 on the number line?

Draw a line AB by measuring 9.3cm.

From the point, B add 1cm and mark it as C.

Mark the point of bisection by a compass and say it as 'O'

Measure AO which is the radius and draws a semi-circle.

From B draw a perpendicular AB touching the semi-circle and mark as D.