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.
$(i)$ Every whole number is a natural number.
$(ii)$ Every integer is a rational number.
$(iii)$ Every rational number is an integer.
(N/A) $(i)$ False,because $0$ is a whole number but not a natural number.
$(ii)$ True,because every integer $m$ can be expressed in the form $\frac{m}{1}$,where $m$ is an integer and $1$ is a non-zero integer,so it is a rational number.
$(iii)$ False,because $\frac{3}{5}$ is a rational number but it is not an integer.
$(ii)$ True,because every integer $m$ can be expressed in the form $\frac{m}{1}$,where $m$ is an integer and $1$ is a non-zero integer,so it is a rational number.
$(iii)$ False,because $\frac{3}{5}$ is a rational number but it is not an integer.
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Is zero a rational number? Can you write it in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$?
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View SolutionState 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.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number.
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View SolutionSimplify each of the following expressions:
$(i)$ $(3+\sqrt{3})(2+\sqrt{2})$
$(ii)$ $(3+\sqrt{3})(3-\sqrt{3})$
$(iii)$ $(\sqrt{5}+\sqrt{2})^{2}$
$(iv)$ $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$
$(i)$ $(3+\sqrt{3})(2+\sqrt{2})$
$(ii)$ $(3+\sqrt{3})(3-\sqrt{3})$
$(iii)$ $(\sqrt{5}+\sqrt{2})^{2}$
$(iv)$ $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$
Medium
View SolutionSimplify the following expressions :
$(i)$ $(5+\sqrt{7})(2+\sqrt{5})$
$(ii)$ $(5+\sqrt{5})(5-\sqrt{5})$
$(iii)$ $(\sqrt{3}+\sqrt{7})^{2}$
$(iv)$ $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$
$(i)$ $(5+\sqrt{7})(2+\sqrt{5})$
$(ii)$ $(5+\sqrt{5})(5-\sqrt{5})$
$(iii)$ $(\sqrt{3}+\sqrt{7})^{2}$
$(iv)$ $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$
Easy
View SolutionFind:
$(i)$ $2^{2/3} \cdot 2^{1/5}$
$(ii)$ $(1/3^3)^7$
$(iii)$ $11^{1/2} / 11^{1/4}$
$(iv)$ $7^{1/2} \cdot 8^{1/2}$
$(i)$ $2^{2/3} \cdot 2^{1/5}$
$(ii)$ $(1/3^3)^7$
$(iii)$ $11^{1/2} / 11^{1/4}$
$(iv)$ $7^{1/2} \cdot 8^{1/2}$
Easy
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