Locate $\sqrt 3$ on the number line.
Locate $\sqrt 3$ on the number line.
Construct $BD$ of unit length perpendicular to $OB$ (as in Fig.). Then using the Pythagoras theorem, we see that $OD =\sqrt{(\sqrt{2})^{2}+1^{2}}=\sqrt{3}$. Using a compass, with centre $O$ and radius $OD ,$ draw an arc which intersects the number line at the point $Q$. Then $Q$ corresponds to $\sqrt{3}$.
In the same way, you can locate $\sqrt n$ for any positive integer $n$, after $\sqrt {n - 1}$ has been located.
Similar Questions
Simplify each of the following expressions :
$(i)$ $(3+\sqrt{3})(2+\sqrt{2})$
$(ii)$ $(3+\sqrt{3})(3-\sqrt{3})$
$(iii)$ $(\sqrt{5}+\sqrt{2})^{2}$
$(iv)$ $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$
Simplify each of the following expressions :
$(i)$ $(3+\sqrt{3})(2+\sqrt{2})$
$(ii)$ $(3+\sqrt{3})(3-\sqrt{3})$
$(iii)$ $(\sqrt{5}+\sqrt{2})^{2}$
$(iv)$ $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$
Are the following statements true or false ? Give reasons for your answers.
$(i)$ Every whole number is a natural number.
$(ii)$ Every integer is a rational number.
$(iii)$ Every rational number is an integer.
Are the following statements true or false ? Give reasons for your answers.
$(i)$ Every whole number is a natural number.
$(ii)$ Every integer is a rational number.
$(iii)$ Every rational number is an integer.
Find the decimal expansions of $\frac{10}{3},\, \frac{7}{8}$ and $\frac{1}{7}$.
Find the decimal expansions of $\frac{10}{3},\, \frac{7}{8}$ and $\frac{1}{7}$.
Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$.
Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$.
Show how $\sqrt 5$ can be represented on the number line.
Show how $\sqrt 5$ can be represented on the number line.