State the type of the decimal expansion of $\frac{1}{7}$

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non-terminating recurring

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Express $0 . \overline{4}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$

After rationalizing the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}},$ we get the denominator as

If $a=5+2 \sqrt{6}$ and $b=\frac{1}{a},$ then what will be the value of $a^{2}+b^{2} ?$

Rationalise the denominator in each of the following

$\frac{1}{\sqrt{5}-\sqrt{3}}$

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ upto three places of decimal.

$\frac{6}{\sqrt{6}}$