# Ex.1.5 Q4 Number System Solution - NCERT Maths Class 9

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## Question

Represent \begin{align}\sqrt {9.3} \end{align} on the number line.

Video Solution
Number Systems
Ex 1.5 | Question 4

## Text Solution

Steps:

Draw a line and take $$AB = 9.3$$ units on it.

From $$B$$ measure a distance of $$1$$ unit and mark $$C$$ on the number line. Make the midpoint of $$AC$$ as $$O.$$

With $$‘O’$$ as center and $$OC$$ as radius, draw a semicircle.

At $$B$$, draw a perpendicular to cut the semicircle at $$D$$, with $$B$$ as center and $$BD$$ as radius draw an arc to cut the number line at $$E$$. Taking $$B$$ as the origin the distance $$\text{BE}=\sqrt{9.3}$$ and hence $$E$$ represents $$\sqrt{9.3}$$ . Proof:

\begin{align} \text{A B} &=\text{9.3, B C=1 }\\ \text{A C} &=\text{A B+B C=10.3 }\\ \text{O C} &=\frac{A C}{2}=\frac{10.3}{2}=5.15 \\ \text{O C }&=\text{O D=5.15}\\\text{O B} &=\text{O C}-\rm{B C}=5.15-1=4.15 \end{align}

In right angled\begin{align}\Delta \rm{OBD},\end{align}

\begin{align} \mathrm{BD}^{2} &=\mathrm{OD}^{2}-0 \mathrm{B}^{2}\\ &=(5.15)^{2}-(4.15)^{2} \\ &=(5.15+4.15)(5.15-4.15) \qquad \qquad \rm{Using} \quad a^{2}-b^{2}=(a+b)(a-b) \\ &=9.3 \times 1\\ &=9.3 \\ \mathrm{BD} &=\sqrt{9.3}=\mathrm{BE} \end{align}

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