Question

Represent

\sqrt{2}

&

\sqrt{5}

on number line.

Accepted Answer

To represent irrational numbers on the number line, we draw a right triangle on the number line such that the hypotenuse of the triangle represent the given irrational number.

For this, we choose the other sides of the triangle such that the square root of the sum of the squares of other two sides gives the given irrational number. Because in a right-angle triangle-

$(hypotenuse)^{2} =$ the sum of the squares of the other two sides.

We can write $\sqrt{2} = \sqrt{1 + 1} = \sqrt{1^{2} + 1^{2}}$ . It means the lengths of the other two sides can be $1$ and $1$ .

So, first, we draw a line $AB$ perpendicular to number line such that the length of $AB$ is $1$ unit. Join $OB$ .

Applying Pythagoras theorem,

${OB}^{2} = {OA}^{2} + {AB}^{2} = 1 + 1 = 2 \Rightarrow OB = \sqrt{2}$

Now, we take compass & taking $O$ as centre & $OB$ as radius, cut the number line. The distance $OS$ will represent $\sqrt{2}$ units as shown below-

Similarly, $\sqrt{5}$ can be written as $\sqrt{1 + 4} = \sqrt{1^{2} + 2^{2}}$ . It means the lengths of the other two sides can be $1$ unit and $2$ units.

So, now, we will draw $AB = 2$ units.

Now, we take compass & taking $O$ as centre & $OB$ as radius, cut the number line. The distance $OS$ will represent $\sqrt{5}$ units as shown below-

Represent $\sqrt{2}$ & $\sqrt{5}$ on number line.

Important Questions on Number Systems

Learn and Prepare for any exam you want !

Represent 2 & 5 on number line.

Important Questions on Number Systems

Learn and Prepare for any exam you want !

Represent $\sqrt{2}$ & $\sqrt{5}$ on number line.