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.
Add $2 \sqrt{2}+5 \sqrt{3}$ and $\sqrt{2}-3 \sqrt{3}$
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ?
Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.
Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$.
Rationalise the denominators of the following :
$(i)$ $\frac{1}{\sqrt{7}}$
$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$
$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$
$(iv)$ $\frac{1}{\sqrt{7}-2}$