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.
$(i)$ False, because zero is a whole number but not a natural number.
$(ii)$ True, because every integer m can be expressed in the form $\frac {m }{1}$ , and so it is a rational number.
$(iii)$ False, because $\frac{3}{5}$ is not an integer.
Similar Questions
Multiply $6 \sqrt{5}$ by $2 \sqrt{5}$.
Multiply $6 \sqrt{5}$ by $2 \sqrt{5}$.
Locate $\sqrt 2$ on the number line.
Locate $\sqrt 2$ on the number line.
Simplify
$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{3}}$
$(ii)$ $\left(3^{\frac{1}{5}}\right)^{4}$
$(iii)$ $\frac{7^{\frac{1}{5}}}{7^{\frac{1}{3}}}$
$(iv)$ $13^{\frac{1}{5}} \cdot 17^{\frac{1}{5}}$
Simplify
$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{3}}$
$(ii)$ $\left(3^{\frac{1}{5}}\right)^{4}$
$(iii)$ $\frac{7^{\frac{1}{5}}}{7^{\frac{1}{3}}}$
$(iv)$ $13^{\frac{1}{5}} \cdot 17^{\frac{1}{5}}$
Rationalise the denominator of $\frac{1}{2+\sqrt{3}}$.
Rationalise the denominator of $\frac{1}{2+\sqrt{3}}$.
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 $\sqrt 2,\, \sqrt 3, \,\sqrt 4$, ..............