How do you simplify sqrt5.26?

Write $5.26$ as a fraction, then simplify the square root of that fraction.
$5.26 = \frac{526}{100}$, so
$\sqrt{5.26} = \sqrt{\frac{526}{100}} = \frac{\sqrt{526}}{\sqrt{100}} = \frac{\sqrt{526}}{10}$
$\sqrt{526}$ cannot be simplified.
($526 = 2 \cdot 263$ and is not divisible by perfect squares: 4, 9, 16, 25, and that's enough to check, because ${25}^{2} = 625 > 526$)