Classroom activity (Constructing the 'square root spiral') : Take a large sheet of paper and construct the 'square root spiral' in the following fashion. Start with a point $O$ and draw a line segment $OP_1$ of unit length. Draw a line segment $P_1P_2$ perpendicular to $OP_1$ of unit length (see Fig.). Now draw a line segment $P_2P_3$ perpendicular to $OP_2$. Then draw a line segment $P_3P_4 $ perpendicular to $OP_3$. Continuing in this manner, you can get the line segment $P_{n-1}P_n$ by drawing a line segment of unit length perpendicular to $OP_{n-1}$. In this manner, you will have created the points $P_2$, $P_3$,...., $P_n$,... ., and joined them to create a beautiful spiral depicting $\sqrt 2,\, \sqrt 3, \,\sqrt 4$, ..............
Classroom activity (Constructing the 'square root spiral') : Take a large sheet of paper and construct the 'square root spiral' in the following fashion. Start with a point $O$ and draw a line segment $OP_1$ of unit length. Draw a line segment $P_1P_2$ perpendicular to $OP_1$ of unit length (see Fig.). Now draw a line segment $P_2P_3$ perpendicular to $OP_2$. Then draw a line segment $P_3P_4 $ perpendicular to $OP_3$. Continuing in this manner, you can get the line segment $P_{n-1}P_n$ by drawing a line segment of unit length perpendicular to $OP_{n-1}$. In this manner, you will have created the points $P_2$, $P_3$,...., $P_n$,... ., and joined them to create a beautiful spiral depicting $\sqrt 2,\, \sqrt 3, \,\sqrt 4$, ..............
Similar Questions
Add $2 \sqrt{2}+5 \sqrt{3}$ and $\sqrt{2}-3 \sqrt{3}$
Add $2 \sqrt{2}+5 \sqrt{3}$ and $\sqrt{2}-3 \sqrt{3}$
Divide $8 \sqrt{15}$ by $2 \sqrt{3}$
Divide $8 \sqrt{15}$ by $2 \sqrt{3}$
Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$.
Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$.
State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number
State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number
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 $\frac{9}{11}$.