Ex.1.2 Q3 Number System Solution - NCERT Maths Class 9

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Question

Show how \(\begin{align}\sqrt 5 \end{align}\) represented on the number line.

 

 Video Solution
Number Systems
Ex 1.2 | Question 3

Text Solution

What is known?

Integer \(5\).

What is unknown?

Point representing \(\begin{align}\sqrt 5 \end{align}\) on the number line.

Steps:

We shall write \(5\) on the sum of two squares in the form \(\begin{align}5=2^{2}+1^{2}=4+1=5 \end{align}\). This shows we need to construct a right triangle with sides \(2\) and \(1\) units. So the hypotenuse becomes \(\begin{align} \sqrt{5} \end{align}\) units on the number line. We shall proceed as follows.

Diagram

On the number line take \(2\) units from \(O\) and represent the point as \(A\). At \(A\) draw the perpendicular and mark \(B\) such that \(\begin{align} AB =1\end{align}\) unit with \(O\) as center and \(\begin{align} OB\end{align}\) as radius. Draw an arc to cut the number line at \(C\). Now \(C\) represents \(\begin{align}\sqrt 5 \end{align}\).

In \(\Delta OAB,\)

\[\begin{align}   O{{B}^{2}}&=O{{A}^{2}}+A{{B}^{2}} \\  &={{2}^{2}}+{{1}^{2}} \\  &=5 \\  \therefore OB &=\sqrt{5}=OC \\ \end{align}\]

 Video Solution
Number Systems
Ex 1.2 | Question 3
  
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