Find the value of $b$ :
$\frac{\sqrt{2}+\sqrt{3}}{3 \sqrt{2}-2 \sqrt{3}}=2-b \sqrt{6}$
$\frac{5}{6}$
$-\frac{2}{6}$
$-\frac{5}{6}$
$\frac{3}{6}$
Simplify: $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$
The number obtained on rationalizing the denominator of $\frac{1}{7-\sqrt{2}}$ is
Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.1 \overline{134}$
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.
$\frac{6}{\sqrt{6}}$
Fill in the blanks so as to make each of the following statements true (Final answer only)
$\sqrt{1 \frac{25}{144}}=\ldots \ldots$