Show how $\sqrt 5$ can be represented on the number line.

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We know that $\sqrt{4}=2$

Let $OA$ be a line of length $2$ unit on the number line. 

Now, construct $AB$ of unit length perpendicular to $OA$. and join $OB$.

Now, in right angle triangle $OAB$, by Pythagoras theorem

Now,  take $O$ as centre and $OB$ as radius, draw an arc intersecting number line at $C$. 

Point $C$ represent $\sqrt{5} $ on a number line.

1098-s11

Similar Questions

Write the following in decimal form and say what kind of decimal expansion each has :

$(i)$ $\frac{36}{100}$

$(ii)$ $\frac{1}{11}$

$(iii)$ $4 \frac{1}{8}$

$(iv)$ $\frac{3}{13}$

$(v)$ $\frac{2}{11}$

$(vi)$ $\frac{329}{400}$

Find :

$(i)$ $9^{\frac{3}{2}}$

$(ii)$ $32^{\frac{2}{5}}$

$(iii)$ $16^{\frac{3}{4}}$

$(iv)$ $125^{\frac{-1}{3}}$

Divide $8 \sqrt{15}$ by $2 \sqrt{3}$

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ?

Simplify the following expressions :

$(i)$ $(5+\sqrt{7})(2+\sqrt{5})$

$(ii)$ $(5+\sqrt{5})(5-\sqrt{5})$

$(iii)$ $(\sqrt{3}+\sqrt{7})^{2}$

$(iv)$ $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$