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\frac{\sqrt{567}}{\sqrt{100}}
Rewrite the square root of the division \sqrt{\frac{567}{100}} as the division of square roots \frac{\sqrt{567}}{\sqrt{100}}.
\frac{9\sqrt{7}}{\sqrt{100}}
Factor 567=9^{2}\times 7. Rewrite the square root of the product \sqrt{9^{2}\times 7} as the product of square roots \sqrt{9^{2}}\sqrt{7}. Take the square root of 9^{2}.
\frac{9\sqrt{7}}{10}
Calculate the square root of 100 and get 10.