The value of $\frac{\sqrt{0.6912} + \sqrt{0.5292}}{\sqrt{0.6912} - \sqrt{0.5292}}$ is:

15

$\frac{\sqrt{0.6912} + \sqrt{0.5292}}{\sqrt{0.6912} - \sqrt{0.5292}}$

we can eliminate the LCM form the numerator and denominator because the places are the same after decimal.

= $\frac{\sqrt{6912} + \sqrt{5292}}{\sqrt{6912} - \sqrt{5292}}$

Take 12 as common from numerator and denominator.

= $\frac{\sqrt{576} + \sqrt{441}}{\sqrt{576} - \sqrt{441}}$

= $\frac{24 + 21}{24 - 21}$

= $\frac{45}{3}$  = 15