Check whether $7 \sqrt{5}, \,\frac{7}{\sqrt{5}}, \,\sqrt{2}+21, \,\pi-2$ are irrational numbers or not.
Check whether $7 \sqrt{5}, \,\frac{7}{\sqrt{5}}, \,\sqrt{2}+21, \,\pi-2$ are irrational numbers or not.
$\sqrt{5}=2.236 \ldots, \sqrt{2}=1.4142 \ldots, \pi=3.1415 \ldots$
Then $7 \sqrt{5}=15.652 \ldots, \frac{7}{\sqrt{5}}=\frac{7 \sqrt{5}}{\sqrt{5} \sqrt{5}}=\frac{7 \sqrt{5}}{5}=3.1304 \ldots$
$\sqrt{2}+21=22.4142 \ldots, \pi-2=1.1415 \ldots$
All these are non-terminating non-recurring decimals. So, all these are irrational numbers.
Similar Questions
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
Is zero a rational number ? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$ ?
Is zero a rational number ? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$ ?
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 :
$(i)$ $(3+\sqrt{3})(2+\sqrt{2})$
$(ii)$ $(3+\sqrt{3})(3-\sqrt{3})$
$(iii)$ $(\sqrt{5}+\sqrt{2})^{2}$
$(iv)$ $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$
Visualise $4. \overline{26}$ . on the number line, up to $4$ decimal places.
Visualise $4. \overline{26}$ . on the number line, up to $4$ decimal places.
Look at several examples of rational numbers in the form $\frac{p}{q}(q \neq 0),$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess what property $q$ must satisfy ?
Look at several examples of rational numbers in the form $\frac{p}{q}(q \neq 0),$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess what property $q$ must satisfy ?