Question

Locate

\sqrt{10}

and

\sqrt{17}

on the number line.

Accepted Answer

Locate $\sqrt{10}$ on a number line,

Using Pythagoras theorem

We can write the $\sqrt{10}$ as below,

$\sqrt{10} = \sqrt{9 + 1}$

This can be written as $\sqrt{10} = \sqrt{3^{2} + 1^{2}}$

The construction steps are shown below:

Take a line segment AO $= 3$ units on x axis. Here consider $1$ unit $= 2 cm$

Draw a perpendicular on O, name it as OC such that OC $= 1$ unit

Now, join AC with $\sqrt{10} .$

Now, take A as centre and AC as radius, draw an arc which cuts the x axis at point E

The line segment AC in the below diagram represents $\sqrt{10}$ units.

Locate $\sqrt{17}$ on a number line,

Using Pythagoras theorem

We can write the $\sqrt{17}$ as below,

$\sqrt{17} = \sqrt{16 + 1} = \sqrt{4^{2} + 1^{2}}$

So, by Pythagoras if we consider A as base and $1$ as perpendicular then hypoteous will be $17 .$

Step 1: Draw number line and mark $4$ on this line.

Step 2: Draw a line perpendicular to number line from $4$ mark and join of this to $0 .$

Step 3: Hypothenous will be $\sqrt{17}$ and mark an arc of this $\sqrt{17}$ on number line.

Hence, the required answer is shown above.

M L Aggarwal Solutions for Chapter: Number System, Exercise 2: Exercise 1.2

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Number System, Exercise 2: Exercise 1.2

Questions from M L Aggarwal Solutions for Chapter: Number System, Exercise 2: Exercise 1.2 with Hints & Solutions

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