If $\left(\frac{2}{5}\right)^{5} \times\left(\frac{25}{4}\right)^{3}=\left(\frac{5}{2}\right)^{3 x-2},$ then find $x$.
$11$
$7$
$3$
$1$
Fill in the blanks so as to make each of the following statements true (Final answer only)
$\sqrt{1 \frac{25}{144}}=\ldots \ldots$
Value of $(256)^{0.16} \times(256)^{\operatorname{0.09}}$ is
Fill in the blanks so as to make each of the following statements true (Final answer only)
$\sqrt{2} \cdot \sqrt{3} \cdot \sqrt{6}=\ldots \ldots .$
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.
$\frac{\sqrt{10}-\sqrt{5}}{2}$
If $x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ and $y=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}},$ then find the value of $x^{2}+y^{2}$.