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\left(\sqrt{\sqrt{27}}\right)^{2}
Multiply \sqrt{\sqrt{27}} and \sqrt{\sqrt{27}} to get \left(\sqrt{\sqrt{27}}\right)^{2}.
\left(\sqrt{3\sqrt{3}}\right)^{2}
Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.
3\sqrt{3}
Calculate \sqrt{3\sqrt{3}} to the power of 2 and get 3\sqrt{3}.