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\sqrt{49+\sqrt[3]{\left(-5\right)^{3}}}
Calculate -7 to the power of 2 and get 49.
\sqrt{49+\sqrt[3]{-125}}
Calculate -5 to the power of 3 and get -125.
\sqrt{49-5}
Calculate \sqrt[3]{-125} and get -5.
\sqrt{44}
Subtract 5 from 49 to get 44.
2\sqrt{11}
Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.