For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$\frac{\sqrt{50}}{\sqrt{98}}$ is a $\ldots \ldots \ldots$ number.

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$4 . \overline{185}=\ldots \ldots$

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.

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

Simplify: $\frac{7 \sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2 \sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3 \sqrt{2}}{\sqrt{15}+3 \sqrt{2}}$

Find the value of $a$ :

$\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$

Simplify the following expressions

$(3+\sqrt{5})(4-\sqrt{11})$