Are the square roots of all positive integers irrational ? If not, give an example of the square root of a number that is a rational number.
Are the square roots of all positive integers irrational ? If not, give an example of the square root of a number that is a rational number.
If numbers such as $\sqrt{4}=2,\, \sqrt{9}=3$ are considered, Then here, $2$ and $3$ are rational numbers. Thus, the square roots of all positive integers are not irrational.
Similar Questions
Divide $8 \sqrt{15}$ by $2 \sqrt{3}$
Divide $8 \sqrt{15}$ by $2 \sqrt{3}$
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ?
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ?
Classify the following numbers as rational or irrational :
$(i)$ $\sqrt{23}$
$(ii)$ $\sqrt{225}$
$(iii)$ $0.3796$
$(iv)$ $7.478478 \ldots$
$(v)$ $1.101001000100001 \ldots$
Classify the following numbers as rational or irrational :
$(i)$ $\sqrt{23}$
$(ii)$ $\sqrt{225}$
$(iii)$ $0.3796$
$(iv)$ $7.478478 \ldots$
$(v)$ $1.101001000100001 \ldots$
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 ?
Express the following in the form $\frac {p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0 . \overline{6}$
$(ii)$ $0 . 4\overline{7}$
$(iii)$ $0 . \overline{001}$
Express the following in the form $\frac {p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0 . \overline{6}$
$(ii)$ $0 . 4\overline{7}$
$(iii)$ $0 . \overline{001}$