Show how $\sqrt 5$ can be represented on the number line.
Show how $\sqrt 5$ can be represented on the number line.
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.
Similar Questions
Write the following in decimal form and say what kind of decimal expansion each has :
$(i)$ $\frac{36}{100}$
$(ii)$ $\frac{1}{11}$
$(iii)$ $4 \frac{1}{8}$
$(iv)$ $\frac{3}{13}$
$(v)$ $\frac{2}{11}$
$(vi)$ $\frac{329}{400}$
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 :
$(i)$ $9^{\frac{3}{2}}$
$(ii)$ $32^{\frac{2}{5}}$
$(iii)$ $16^{\frac{3}{4}}$
$(iv)$ $125^{\frac{-1}{3}}$
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 $2 \sqrt{3}$
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 $\frac{1}{17}$ ?
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 :
$(i)$ $(5+\sqrt{7})(2+\sqrt{5})$
$(ii)$ $(5+\sqrt{5})(5-\sqrt{5})$
$(iii)$ $(\sqrt{3}+\sqrt{7})^{2}$
$(iv)$ $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$
Simplify the following expressions :
$(i)$ $(5+\sqrt{7})(2+\sqrt{5})$
$(ii)$ $(5+\sqrt{5})(5-\sqrt{5})$
$(iii)$ $(\sqrt{3}+\sqrt{7})^{2}$
$(iv)$ $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$